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  • Find the intervals on which the function is (a) strictly increasing (b) strictly decreasing.

Find the intervals on which the function f(x) = (x - 1)^{3} (x - 2)^2 is (a) strictly increasing (b) strictly decreasing.

 

Answers (1)

f(x) = (x - 1)^{3} (x - 2)^2

f'(x) = 3(x - 1)^{2} (x - 2)^2 + 2(x - 1)^{3} (x - 2)

f'(x) = (x - 1)^{2} (x - 2)(3x-6 + 2x - 2)

f'(x) = (x - 1)^{2} (x - 2)(5x- 8)

(a) strictly increasing

f'(x) = (x - 1)^{2} (x - 2)(5x- 8)>0

x \in(-\infty, 1) \cup\left(1, \frac{8}{5}\right) \cup(2, \infty)

(b) strictly decreasing.

f'(x) = (x - 1)^{2} (x - 2)(5x- 8)<0

x \in\left(\frac{8}{5}, 2\right)

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Safeer PP

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