# Finding the Critical Point and Relative Minimum and Maximum

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Consider the function f(x) = 4kx^(3) - (k^2 - 13)x + 9k, where k is a constant.

(a) Suppose that f has a critical point at x = 1. Find all possible value(s) of k. If there is more than one answer, enter them separated by commas.

Answer: f has a critical point at x = 1 exactly when k = ______

(b) If f has a relative maximum at x = 1, find all possible value(s) of k. If there is more than one answer, enter them separated by commas.

Answer: f has a relative maximum at x = 1 exactly when k=______

(c) If f has a relative minimum at x = 1, find all possible value(s) of k. If there is more than one answer, enter them separated by commas.

Answer: f has a relative minimum at x = 1 exactly when k = _______.

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Solution provides steps necessary to calculate the critical point, the relative minimum and the relative maximum.

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Consider the function f(x) = 4kx^3 - (k^2 - 13)x + 9k, where k is a constant.

(a) Suppose that f has a critical point at x = 1. Find all possible value(s) of k. If there is more than one answer, enter them separated by commas.

We have f^'(x) = 12kx^2 - (k^2 - 13)

Suppose that f ...

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