What is the extreme f(x)=-x^3+3x^2+45x-7 ?

The extreme f(x)=-x^3+3x^2+45x-7 is Minimum(-3,-88),Maximum(5,168)

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extreme f(x)=-x^3+3x^2+45x-7

extreme points

f (x) = - x^{3} + 3 x^{2} + 45 x - 7

Minimum (- 3, - 88), Maximum (5, 168)

Solution steps

f^{'} (x) = - 3 x^{2} + 6 x + 45

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = - 3

into

- x^{3} + 3 x^{2} + 45 x - 7 : - 88

Minimum (- 3, - 88)

Plug

x = 5

into

- x^{3} + 3 x^{2} + 45 x - 7 : 168

Maximum (5, 168)

Minimum (- 3, - 88), Maximum (5, 168)

What is the extreme f(x)=-x^3+3x^2+45x-7 ?
The extreme f(x)=-x^3+3x^2+45x-7 is Minimum(-3,-88),Maximum(5,168)