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. one of these values is x = 4. for what other value is f (x) = 0? f (x) = 0 at x = 4 and x =
Answer
Explanation:
Step1: Recall derivative meaning
The derivative $f^{\prime}(x)$ is the slope of the tangent - line to the graph of $y = f(x)$ at the point $(x,f(x))$.
Step2: Analyze slope 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 $f^{\prime}(x)=0$ when the tangent line to the graph of $y = f(x)$ is horizontal.
Step4: Find other $x$ value
Looking at the graph, the tangent line is horizontal at the peak of the graph. The peak occurs at $x = 10$. So $f^{\prime}(x) = 0$ at $x = 10$.
Answer:
a. A. $f^{\prime}(1)>f^{\prime}(2)$ b. $10$