Let f :R→R be a differentiable function, such that the secant line through any two points on its graph has negative slope. Then ... (Select all that apply.) O f'(x) could be zero for some value of x. O f'(x) could be zero for all x's . O f'(x) must be negative for some value of x. O f'(x) must be negative all x 's .

Q: Suppose f is a differentiable function such that f(-2) = 3 and f(5) = 17. Then there must be a point…

A: Consider the conditions for the mean value theorem.

Q: The figure below shows the derivative F' of F. Let F (0) = 0. F'(1) ਜਿਹ 8 + 2 4 6 Of the four…

A:

Q: Let f(x) f'(2)= | ƒ' (6)= Lomm 7 Vx Evaluate each of the following: I

A:

Q: Suppose f and g are functions that are differentiable at x=5 and that f(5)=8 ,f'(5)=-3 ,g(5)=-1 ,…

A:

Q: Find f'(x) for f(x) = ex²+3x+¹¸

A: Given that f(x)=ex2+3x+1

Q: 1. Sketch a function f(x) with the following properties: • f'(x) > 0 and f"(x) = 0, for x 2

A: As you posted multiple question , I need to solve only first question.

Q: 6. Apply the First-Derivative Test, to identify all relative extrema of f(x) = x3- Answe homev 16…

A: Given query is to find the relative extrime.

Q: 1. Determine f'(x) for the following functions: f(x) = (x2 – 3x)5 b. f(x) = V1-x²

A:

Q: The graph of f'(x) is shown below. Give the interval(s) where the graph of f(x) is concave up. y =f…

A:

Q: Select the graph of a function f that satisfies f' 0 on (-0, -1)U(-1, 0).

A: means f is decreasing for x> - 1   means f(x) is concave up on both sides of x=-1

Q: Let f'(x) = x³ - 9x² +24x +3.

A:

Q: Find f' in terms of g' if (i) f(x) = g(x + g(a)). %3D

A: We will use the formula f(g(x))' = f'(g(x))g'(x)

Q: f(3.8) - If we knew that f"(x) < 0 on the interval (3.5, 4.5), would your estimate above be an…

A: We need to find f(3.8)