question 9 of 10 view policies current attempt in progress at exactly two of the labeled points in the…

question 9 of 10 view policies current attempt in progress at exactly two of the labeled points in the figure below, the derivative $f$ is 0; the second derivative $f$ is not zero at any of the labeled points. give the signs of $f$, $f$, $f$ at each marked point. etextbook and media save for later using multiple attempts will impact your score. 5% score reduction after attempt 5 attempts: 0 of 15 used submit answer

question 9 of 10 view policies current attempt in progress at exactly two of the labeled points in the figure below, the derivative $f$ is 0; the second derivative $f$ is not zero at any of the labeled points. give the signs of $f$, $f$, $f$ at each marked point. etextbook and media save for later using multiple attempts will impact your score. 5% score reduction after attempt 5 attempts: 0 of 15 used submit answer

Answer

Explanation:

Step1: Analyze point A

The function value (f(A)) is below the (x -)axis, so (f(A)<0). The slope of the tangent line at (A) is positive, so (f'(A)>0). The curve is concave - down at (A), so (f''(A)<0).

Step2: Analyze point B

The function value (f(B)) is above the (x -)axis, so (f(B)>0). The slope of the tangent line at (B) is (0) (local maximum), so (f'(B) = 0). The curve is concave - down at (B), so (f''(B)<0).

Step3: Analyze point C

The function value (f(C)) is above the (x -)axis, so (f(C)>0). The slope of the tangent line at (C) is negative, so (f'(C)<0). The curve is concave - down at (C), so (f''(C)<0).

Step4: Analyze point D

The function value (f(D)) is below the (x -)axis, so (f(D)<0). The slope of the tangent line at (D) is (0) (local minimum), so (f'(D)=0). The curve is concave - up at (D), so (f''(D)>0).

Answer:

Point (f) (f') (f'')
(A) Negative Positive Negative
(B) Positive Zero Negative
(C) Positive Negative Negative
(D) Negative Zero Positive