Consider the graph of f. 4 3 y + 1 2 3 4 5 6 7 8 9 +X Determine the correct statement(s) about f'(x). ƒ'(8.5) < ƒ'(6.5) f'(4.5) > f'(5.5) ƒ'(8.5) < f'(2.5) f'(4.5) < f'(5.5) ƒ' (8.5) > ƒ' (6.5) f'(7.5) = f'(2.5) ƒ' (5.5) = f'(4.5)

4 For the function f(x) evaluate and simplify the Difference Quotient. SHOW ALL WORK. a) Solution: Difference Quotient = b) Use the difference quotient to find the average rate of change of the function f(x) over the interval (3, 3 + h), where h = 1: slope of secant line ; {Give at least 4 decimal places} and also h .1: slope of secant line %3D . {Give at least 4 decimal places} Sketch each of these situations in your Notebooks. c) What value of h will produce a secant line with a slope of -0.4443 over the interval from 3, 3 + h? h {Give at least 4 decimal places when needed.}

Please solve and show all work, thank you!!

☐ 2. The figure below shows the graphs of f(x), f'(x), and ƒ"(x). Identify each ☐ 3. The figure below shows the graphs of f(x), f'(x), and f" (x). Identify each curve. orange Choices f(x) blue f'(x) black ƒ"(x) -2 black Choices blue orange R f(x) f'(x) f"(x) 6. The figure below shows the graphs of f(x), f'(x), and f" (x). Identify each curve. -2 black Choices f(x) blue f'(x) orange ƒ"(x)

Create a sequence of secant lines that can be used to approximate the value of the derivative at x =-1. Give your values of h and the slope of the secant line for that value of h. Now think about the derivative of f (x) = 2 Caution: The graph of the function f(x) = 2* is still depicted below. h slope of secant line You can approximate the value of the derivative at x= a by looking at the slopes of the secant lines very close to the input a. That is for small values of h, find the slope of the secant line on the interval [a, a + h] 10 Create a sequence of secant lines that can be used to approximate the value of the derivative at x = 0. Give your values of h and the slope of the secant line for that value of h. -8 h slope of secant line Create a sequence of secant lines that can be used to approximate the value of the derivative at x = 1. Give your values of h and the slope of the secant line for that value of h. -4 3 -2 -1 h slope of secant line