What is the extreme f(x)=2x^3+12x^2-192x-45 ?

The extreme f(x)=2x^3+12x^2-192x-45 is Maximum(-8,1235),Minimum(4,-493)

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extreme f(x)=2x^3+12x^2-192x-45

extreme points

f (x) = 2 x^{3} + 12 x^{2} - 192 x - 45

Maximum (- 8, 1235), Minimum (4, - 493)

Solution steps

f^{'} (x) = 6 x^{2} + 24 x - 192

Find intervals:

Increasing

: - \infty < x < - 8,

Decreasing

: - 8 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = - 8

into

2 x^{3} + 12 x^{2} - 192 x - 45 : 1235

Maximum (- 8, 1235)

Plug

x = 4

into

2 x^{3} + 12 x^{2} - 192 x - 45 : - 493

Minimum (4, - 493)

Maximum (- 8, 1235), Minimum (4, - 493)

x^{4} - x^{5}

- 2 e^{- 2 x} (x^{4} - 2 x^{3})

f (x) = x^{4} + 6 x^{3} - 5 x^{2} + 2 x + 3

f (x) = x^{2} - 8 x + 17

f (x) = 8 x^{2} - x^{4}

What is the extreme f(x)=2x^3+12x^2-192x-45 ?
The extreme f(x)=2x^3+12x^2-192x-45 is Maximum(-8,1235),Minimum(4,-493)