What is the extreme f(x)=3x^3+9x^2-72x ?

The extreme f(x)=3x^3+9x^2-72x is Maximum(-4,240),Minimum(2,-84)

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extreme f(x)=3x^3+9x^2-72x

extreme points

f (x) = 3 x^{3} + 9 x^{2} - 72 x

Maximum (- 4, 240), Minimum (2, - 84)

Solution steps

f^{'} (x) = 9 x^{2} + 18 x - 72

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 4

into

3 x^{3} + 9 x^{2} - 72 x : 240

Maximum (- 4, 240)

Plug

x = 2

into

3 x^{3} + 9 x^{2} - 72 x : - 84

Minimum (2, - 84)

Maximum (- 4, 240), Minimum (2, - 84)

f (x y) = x^{2} y^{3} - 2 x^{4} y

f (x) = x^{2} + 2 y^{2} - x y + 14 y

f (x) \frac{1}{( x ^{2} - 10 x + 35 ) ^{3}}

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

f (x) = x^{2} - 10 x - 1, 2 \leq x \leq 6

What is the extreme f(x)=3x^3+9x^2-72x ?
The extreme f(x)=3x^3+9x^2-72x is Maximum(-4,240),Minimum(2,-84)