**positive**on the given interval.

Is conceive plus the same as pre seed?

**how long does pre seed last inside you**.

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This is equivalent to the derivative of f′ , which is f′′f, start superscript, prime, prime, end superscript, being positive. Similarly, f is **concave down** (or downwards) where the derivative f′ is decreasing (or equivalently, f′′f, start superscript, prime, prime, end superscript is negative).

A concave up **position versus time graph has positive acceleration**. The reason can be seen by considering the case of a system with constant positive acceleration. The position versus time graph for such a system will be an upward-opening parabola like that shown below.

If f “(x) > 0, the graph is concave upward at that value of x. If f “(x) = 0, the graph may have a point of inflection at that value of x. To check, consider the value of f “(x) at values of x to either side of the point of interest. If f “(x) < 0, the graph is **concave downward** at that value of x.

If a function is decreasing and concave up, then its rate of decrease is slowing; it is “leveling off.” If the function is increasing and concave up, then the rate of increase is **increasing**. The function is increasing at a faster and faster rate. Now consider a function which is concave down.

Taking the second derivative actually tells us if the slope continually increases or decreases. When the second derivative **is positive, the function is concave upward**. When the second derivative is negative, the function is concave downward.

Here’s a video by patrickJMT showing you how the second derivative test can tell us the concavity of a function. A function is concave up (or convex) **if it bends upwards**. A function is concave down (or just concave) if it bends downwards.

The shape of a production possibility curve (PPC) reveals important information about the opportunity cost involved in producing two goods. … When the PPC is concave (**bowed out**), opportunity costs increase as you move along the curve. When the PPC is convex (bowed in), opportunity costs are decreasing.

We would then describe the **production function as convex rather than concave**. A special case is the function y=Ah2: you can check by differentiating that for this production function, the graph of the marginal product of labour is an upward-sloping straight line.

The second derivative is **the rate of change of the rate of change of a point at a graph** (the “slope of the slope” if you will). This can be used to find the acceleration of an object (velocity is given by first derivative).

- If f′(x)>0 on an open interval, then f is increasing on the interval.
- If f′(x)<0 on an open interval, then f is decreasing on the interval.

To find when a function is concave, you **must first take the 2nd derivative, then set it equal to 0, and then find between which zero values the function is negative**. Now test values on all sides of these to find when the function is negative, and therefore decreasing.

A function can be concave up and **either increasing or decreasing**. Similarly, a function can be concave down and either increasing or decreasing.

The first derivative of a function is an expression which tells us **the slope of a tangent line to the curve at any instant**. Because of this definition, the first derivative of a function tells us much about the function. If is positive, then must be increasing. If is negative, then must be decreasing.

The second derivative is zero **(f (x) = 0):** When the second derivative is zero, it corresponds to a possible inflection point. If the second derivative changes sign around the zero (from positive to negative, or negative to positive), then the point is an inflection point.

What we usually call a “bell-shaped” graph, is **neither concave** (or “concave down”) nor convex (or “concave up”) -it has both concave and convex parts. the above is certainly negative irrespective of the value of x (and so the density graph will be concave for the whole of its domain).

A function is said to be concave upward on an interval if **f″(x) > 0 at each point in the interval** and concave downward on an interval if f″(x) < 0 at each point in the interval. … Geometrically, a function is concave upward on an interval if its graph behaves like a portion of a parabola that opens upward.

In mathematics, a concave function is **the negative of a convex function**. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap, or upper convex.

A function of a single variable is **concave if every line segment joining two points on its graph does not lie above the graph at any point**. Symmetrically, a function of a single variable is convex if every line segment joining two points on its graph does not lie below the graph at any point.

**Concave means** “hollowed out or rounded inward” and is easily remembered because these surfaces “cave” in. The opposite is convex meaning “curved or rounded outward.” Both words have been around for centuries but are often mixed up. Advice in mirror may be closer than it appears.

The first is the fact that the budget constraint is a straight line. This is because its slope is given by the relative prices of the two goods. In contrast, the PPF has a curved shape **because of the law of the diminishing returns**. The second is the absence of specific numbers on the axes of the PPF.

Its always drawn as a curve and not a straight line **because there a cost involved in making a choice i.e** when the quantity of one good produced is higher and the quantity of the other is low. This is known as opportunity cost.

A utility function is **quasi–concave** if and only if the preferences represented by that utility function are convex. A utility function is strictly quasi–concave if and only if the preferences represented by that utility function are strictly convex.

Preferences are convex if **and only if the corresponding utility function is quasi-concave**. Assume preferences satisfy completeness, transitivity, continuity and monotonicity.

A non-convex function is **wavy – has some ‘valleys’ (local minima) that aren’t as deep as the overall deepest ‘valley’** (global minimum). Optimization algorithms can get stuck in the local minimum, and it can be hard to tell when this happens.

The sign of **the derivative will indicate negative when the function is decreasing and positive when the function is increasing**. The screen will also indicate a zero derivative. Students will need to edit the function on the screen in order to investigate other functions.

2) The third derivative, or higher derivatives for that matter, are generally used **to improve the accuracy of an approximation to the function**. Taylor’s expansion of a function around a point involves higher order derivatives, and the more derivatives you consider, the higher the accuracy.

The positive regions of a function are those **intervals where the function is above the x-axis**. It is where the y-values are positive (not zero). The negative regions of a function are those intervals where the function is below the x-axis. … y-values that are on the x-axis are neither positive nor negative.

When a function is always increasing, we say the function is **a strictly increasing function**. When a function is increasing, its graph rises from left to right. If you can’t observe the graph of a function, you can check the derivative of the function to determine if it’s increasing.

The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If **f′(x) > 0 at each point in an interval I**, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.

The second derivative tells whether the curve is concave up or concave down at that point. If the second derivative is positive at a point, the graph is bending upwards at that point. Similarly if the second derivative is negative, the graph **is concave down**.

If the tangent line between the point of tangency and the approximated point is below the curve (that is, the curve is concave up) the **approximation is an underestimate** (smaller) than the actual value; if above, then an overestimate.)

- Find the second derivative of f.
- Set the second derivative equal to zero and solve.
- Determine whether the second derivative is undefined for any x-values. …
- Plot these numbers on a number line and test the regions with the second derivative.

If f″(x) is positive on an interval, the graph of **y=f(x) is concave up on that interval**. We can say that f is increasing (or decreasing) at an increasing rate. If f″(x) is negative on an interval, the graph of y=f(x) is concave down on that interval.