What is the extreme f(x)=-x^3+6x^2+135x+1 ?

The extreme f(x)=-x^3+6x^2+135x+1 is Minimum(-5,-399),Maximum(9,973)

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extreme f(x)=-x^3+6x^2+135x+1

extreme points

f (x) = - x^{3} + 6 x^{2} + 135 x + 1

Minimum (- 5, - 399), Maximum (9, 973)

Solution steps

f^{'} (x) = - 3 x^{2} + 12 x + 135

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < 9,

Decreasing

: 9 < x < \infty

Plug

x = - 5

into

- x^{3} + 6 x^{2} + 135 x + 1 : - 399

Minimum (- 5, - 399)

Plug

x = 9

into

- x^{3} + 6 x^{2} + 135 x + 1 : 973

Maximum (9, 973)

Minimum (- 5, - 399), Maximum (9, 973)

x^{2} - 8 x + 15

x^{2} - 8 x + 13

f (x) = 2 x^{2} - 5 x + 2

f (x) = \frac{x}{ln ( x )} [2.1]

f (x) = x^{4} - 72 x^{2} - 2, - 7 \leq x \leq 7

What is the extreme f(x)=-x^3+6x^2+135x+1 ?
The extreme f(x)=-x^3+6x^2+135x+1 is Minimum(-5,-399),Maximum(9,973)