What is the extreme f(x)=6x^3+27x^2-180x ?

The extreme f(x)=6x^3+27x^2-180x is Maximum(-5,825),Minimum(2,-204)

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extreme f(x)=6x^3+27x^2-180x

extreme points

f (x) = 6 x^{3} + 27 x^{2} - 180 x

Maximum (- 5, 825), Minimum (2, - 204)

Solution steps

f^{'} (x) = 18 x^{2} + 54 x - 180

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 5

into

6 x^{3} + 27 x^{2} - 180 x : 825

Maximum (- 5, 825)

Plug

x = 2

into

6 x^{3} + 27 x^{2} - 180 x : - 204

Minimum (2, - 204)

Maximum (- 5, 825), Minimum (2, - 204)

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

2 x^{3} - 33 x^{2} + 108 x + 5

f (x) = x^{3} - \frac{3}{2} x^{2}, - 2 \leq x \leq 4

x^{3} - 6 x^{2} + 2 x - 2

What is the extreme f(x)=6x^3+27x^2-180x ?
The extreme f(x)=6x^3+27x^2-180x is Maximum(-5,825),Minimum(2,-204)