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Popular Functions >

extreme f(x)=(x-5)(x-3)(x+1)^2

Solution

extreme

Solution

Minimum (- 1, 0), Maximum (\frac{11 - 33}{4}, \frac{165 33 - 363}{32} + 15), Minimum (\frac{11 + 33}{4}, \frac{- 363 - 165 33}{32} + 15)

Solution steps

f^{'} (x) = 2 (x + 1) (2 x^{2} - 11 x + 11)

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < \frac{11 - 33}{4},

Decreasing

: \frac{11 - 33}{4} < x < \frac{11 + 33}{4},

Increasing

: \frac{11 + 33}{4} < x < \infty

Plug

x = - 1

into

(x - 5) (x - 3) (x + 1)^{2} : 0

Minimum (- 1, 0)

Plug

x = \frac{11 - 33}{4}

into

(x - 5) (x - 3) (x + 1)^{2} : \frac{165 33 - 363}{32} + 15

Maximum (\frac{11 - 33}{4}, \frac{165 33 - 363}{32} + 15)

Plug

x = \frac{11 + 33}{4}

into

(x - 5) (x - 3) (x + 1)^{2} : \frac{- 363 - 165 33}{32} + 15

Minimum (\frac{11 + 33}{4}, \frac{- 363 - 165 33}{32} + 15)

Minimum (- 1, 0), Maximum (\frac{11 - 33}{4}, \frac{165 33 - 363}{32} + 15), Minimum (\frac{11 + 33}{4}, \frac{- 363 - 165 33}{32} + 15)

Graph

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Frequently Asked Questions (FAQ)

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