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At a local maximum of a differentiable function $f$ on its domain:
A$f'(c) > 0$, since slope is positive on the school chart
B$f''(c) > 0$, second derivative is positive on the chart
C$f(c)$ is the smallest value of $f$ near $c$ in the chart
D$f'(c) = 0$, the slope of the tangent is zero on the chart
Answer & Solution
Correct answer: D. $f'(c) = 0$, the slope of the tangent is zero on the chart
At an interior local max of a differentiable function, the derivative is zero.
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