assume the entire graph of f(x) is shown below. use the graph to to complete parts a through c. a. compare f…

assume the entire graph of f(x) is shown below. use the graph to to complete parts a through c. a. compare f ’(1) and f ’(2). select one. a. f ’(1) < f ’(2) b. f ’(1) > f ’(2) c. f ’(1) = f ’(2) b. f ’(x) = 0 at integer values of x. two of these values are x = 4 and x = 12. for what other value is f ’(x) = 0? f ’(x) = 0 at x = 4, x = 12 and x =

assume the entire graph of f(x) is shown below. use the graph to to complete parts a through c. a. compare f ’(1) and f ’(2). select one. a. f ’(1) < f ’(2) b. f ’(1) > f ’(2) c. f ’(1) = f ’(2) b. f ’(x) = 0 at integer values of x. two of these values are x = 4 and x = 12. for what other value is f ’(x) = 0? f ’(x) = 0 at x = 4, x = 12 and x =

Answer

Explanation:

Step1: Recall derivative meaning

The derivative $f^{\prime}(x)$ represents the slope of the tangent - line to the graph of $y = f(x)$ at the point $(x,f(x))$.

Step2: Analyze slopes at $x = 1$ and $x = 2$

At $x = 1$, the graph of $y = f(x)$ is increasing and has a relatively steep positive - slope. At $x = 2$, the graph is still increasing but has a less steep positive - slope. So, $f^{\prime}(1)>f^{\prime}(2)$.

Step3: Recall when derivative is zero

The derivative $f^{\prime}(x)=0$ at the points where the tangent line to the graph of $y = f(x)$ is horizontal.

Step4: Identify horizontal - tangent points

From the graph, we can see that the tangent line is horizontal at $x = 4$, $x = 12$, and also at $x = 8$.

Answer:

a. B. $f^{\prime}(1)>f^{\prime}(2)$ b. 8