the graph of the function f is shown below. at which of the following points is f(x) positive and…
the graph of the function f is shown below. at which of the following points is f(x) positive and decreasing? a d b c
Answer
Answer:
d
Explanation:
Step1: Recall derivative meaning
$f^{\prime}(x)$ is slope of tangent.
Step2: Analyze point a
At a, $f^{\prime}(x)<0$ (negative - sloped tangent).
Step3: Analyze point b
At b, $f^{\prime}(x) = 0$ (horizontal tangent).
Step4: Analyze point c
At c, $f^{\prime}(x)=0$ (horizontal tangent).
Step5: Analyze point d
At d, $f^{\prime}(x)>0$ (positive - sloped tangent) and as we move to the right near d, the slope of the tangent is decreasing.