Problem: The figure above shows the graph f \', the derivative of the function f

Question

Problem: The figure above shows the graph f ', the derivative of the function f, for -7 <(or equal="" to="" x="3.<br" or="" 7="" the="" graph="" of="" f="" has="" horizontal="" tangent="" lines="" at="" and="" a="" vertical="" line="">
Question: Find all values of x, for -7 < x < 7, at which f attains a relative minimum. Justify your answer. Find all values of x, for -7 < x < 7, at which f attains a relative maximum. Justify your answer. Find all values of x, for -7 < x < 7, at which f "(x) < 0.

Explanation / Answer

Since your question seems jumbled, I will explain to you how to do this. All maxima, minima, and plateaus occur when f'=0, so look for points where f' crosses the x-axis between -7 and 7. If x is negative to the left of that point and positive to the right, then it is a minimum.

Otherwise, if x is positive to the left and negative to the right, then x is a local maximum. If f' only touches the x-axis but does not cross it, then it is a plateau.

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