Suppose you are given a formula for a function f. (a) How do you determine where f is increasing or decreasing? If f '(x)  ? < > = 0 on an interval, then f is increasing on that interval. If f '(x)  ? < > = 0 on an interval, then f is decreasing on that interval. (b) How do you determine where the graph of f is concave upward or concave downward? If f ''(x)  ? < > = 0 for all x in I, then the graph of f is concave upward on I. If f ''(x)  ? < > = 0 for all x in I, then the graph of f is concave downward on I. (c) How do you locate inflection points? At any value of x where f '(x) = 0, we have an inflection point at (x, f(x)).At any value of x where the concavity does not change, we have an inflection point at (x, f(x)).     At any value of x where the concavity changes, we have an inflection point at (x, f(x)).At any value of x where the function changes from decreasing to increasing, we have an inflection point at (x, f(x)).At any value of x where the function changes from increasing to decreasing, we have an inflection point at (x, f(x)).

Q: The graph of a function is shown below. Select the graph of the derivative f'.

A: Given, A graph of the function We have to find the graph of the derivative of the function.

Q: Suppose that 2 < f '(x) < 4 for all values of x. What are the minimum and maximum possible values of…

A: (a) Given that 2≤f'(x)≤4 for all values of x. By mean value theorem, if f(x) is continues in a,b and…

Q: If F(x) = f(g(x)), where f(-3) = 5, f'(-3) = 2, f'(1) = 3, g(1) = -3, and g'(1) = 5, find F'(1).…

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Q: Įsin x cos^(3/2) x dx * O -2/5 cos^(5/2) x + C O None of the choices -5/2 cos^(5/2) x + C O -2…

A:

Q: If f'(x) = x(x- 2)(x+1), then the graph of f has points of inflec- tion when x = A. -2 and 1 B. 2…

A: f''(x)= x(x-2)(x+1)2  To find the points of inflection of function f  A. -2 and 1 B. 2 and -1 C. 2…

Q: What information about a graph can be found from the second derivative?

A: What information about a graph can be found from the second derivative?

Q: The following graph corresponds to f"(x), the second derivative of f(x). If the graph does not…

A:

Q: 4 -4 -3 2 4 -2

A: See from the given graph of the function fx, the graph becomes parallel to x axis at the points x=-2…

Q: If f'(x) = (2-2x)e(1-x), which of the following statements is true about the graph of f(x)? Select…

A:

Q: When dealing with graphs of a function, how would you find the original function graph when given a…

A:

Q: SOLVE BY LINEAR METHOD - y'- 3 X Y = x 3 cos (x)

A:

Q: Suppose that for two functions f &amp; g, we know the following information:f(8) = 16f'(8) = 6f(3) =…

A: The given composition function is

Q: If the sign of the first derivative function is positive, the main function f(x) is decreasing.

A: This question related to derivative.

Q: if f(X)=(1-2X)^5 then find f`(X)

A:

Q: From the graph of f(x), determine the graph of f'(x). -6 i पं -3 -2 1 y 5 4 3 2 O -1 -2 -3 -4 -5 2 W…

A: We need to find graph of f'(x) from given graph of f(x).Concept -If f(x) is increasing then slope…

Q: Consider the following. f(x)=x²-6x² + 7

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Q: When looking at the graph of an original function, how do you know when the derivative of the…

A: To find the derivative, for your visualization, just draw the graph and the graph of its derivative.…

Q: Suppose that f is a function given as f(x) = 2x² + 7x - 2. Simplify the expression f(x + h). f(x +…

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Q: Consider the following function. f(x) = x³(x - 8) (a) Make a sign diagram for the first derivative.…

A: Given f(x)=x3(x-8) ⇒f(x)=x4-8x⇒f'(x)=4x3-8            =4(x3-2)            =4(x-23)(x2+23x+223)

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: