What is the extreme x^3-9x^2+15x+3 ?

The extreme x^3-9x^2+15x+3 is Maximum(1,10),Minimum(5,-22)

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extreme x^3-9x^2+15x+3

extreme points

x^{3} - 9 x^{2} + 15 x + 3

Maximum (1, 10), Minimum (5, - 22)

Solution steps

f^{'} (x) = 3 x^{2} - 18 x + 15

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = 1

into

x^{3} - 9 x^{2} + 15 x + 3 : 10

Maximum (1, 10)

Plug

x = 5

into

x^{3} - 9 x^{2} + 15 x + 3 : - 22

Minimum (5, - 22)

Maximum (1, 10), Minimum (5, - 22)

f (x) = 2^{x + 6}

f (x) = 2 x + \frac{2}{x} - 4

f (x) = \frac{2}{3} x + \frac{10}{3}

f (x) = 4 x + 2

4 x^{6} e^{- 3 x} - 3 x^{7} e^{- 3 x}

What is the extreme x^3-9x^2+15x+3 ?
The extreme x^3-9x^2+15x+3 is Maximum(1,10),Minimum(5,-22)