Unit 5 Quiz 1

The function f is continuous on the closed interval [0,12] and differentiable on the open interval (0, 12). Based on the graph, what are all values of x that satisfy the conclusion of the Mean Value Theorem applied to f on the closed interval [0, 12]?

• 4.5 only because this is the value where f(x) equals the rate of change of f on [0, 12]

• 3 and 8 because these are the values where f'(x)=0 on [0, 12]

• 2 and 9 only because these are the values where the instantaneous rate of change of f at those values is equal to the average rate of change of f on [0, 12]

• 2, 4.5 and 9 because these are the values where either the instantaneous rate of change of f at the value is equal to the average rate of change of f on [0, 12] or the value of f(x) is equal to the average rate of change of f on [0,12]

Let f be a differentiable function with a domain of (0, 10). It is known that f'(x), the derivative of f(x), is negative on the intervals (0, 2) and (4, 6) and positive on the intervals (2, 4) and (6, 10). Which of the following statements is true?

• f has no relative minima and three relative maxima

• f has one relative minimum and two relative maxima

• f has two relative minima and one relative maximum

• f has three relative minima and no relative maxima

Find the critical number of the function  $f\left(x\right)=-6x^2+108x+7$  

• x = 18

• x = 9

• x = 84

• x = 14

• x = 7

Determine the open intervals on which the graph of  $f\left(x\right)=3x^2+7x-3$  is concave down or concave up.

• concave down on  $\left(-\infty,\ \infty\right)$  

• concave up on  $\left(-\infty,\ 0\right)$  ; concave down on  $\left(0,\ \infty\right)$  

• concave up on  $\left(-\infty,\ 1\right)$  ; concave down on  $\left(1,\ \infty\right)$  

• concave up on  $\left(-\infty,\ \infty\right)$  

• concave down on  $\left(-\infty,\ 0\right)$ ; concave up on  $\left(0,\ \infty\right)$  

Let g be the function given by  $g\left(x\right)=3x^4-8x^3$ . At what value of x on the closed interval [-2, 2] does g have an absolute maximum?

• -2

• 0

• 2

•  $\frac{8}{3}$