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Popular >

extreme (3-x)(x-5)^2

Solution

extreme points

(3 - x) (x - 5)^{2}

Solution

Minimum (\frac{11}{3}, - \frac{32}{27}), Maximum (5, 0)

Solution steps

f^{'} (x) = - (x - 5) (3 x - 11)

Find intervals:

Decreasing

: - \infty < x < \frac{11}{3},

Increasing

: \frac{11}{3} < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = \frac{11}{3}

into

(3 - x) (x - 5)^{2} : - \frac{32}{27}

Minimum (\frac{11}{3}, - \frac{32}{27})

Plug

x = 5

into

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

Maximum (5, 0)

Minimum (\frac{11}{3}, - \frac{32}{27}), Maximum (5, 0)

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Frequently Asked Questions (FAQ)

What is the extreme (3-x)(x-5)^2 ?
The extreme (3-x)(x-5)^2 is Minimum(11/3 ,-32/27),Maximum(5,0)