What is the extreme y=x^3-9x^2-48x ?

The extreme y=x^3-9x^2-48x is Maximum(-2,52),Minimum(8,-448)

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extreme y=x^3-9x^2-48x

extreme points

y = x^{3} - 9 x^{2} - 48 x

Maximum (- 2, 52), Minimum (8, - 448)

Solution steps

f^{'} (x) = 3 x^{2} - 18 x - 48

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 8,

Increasing

: 8 < x < \infty

Plug

x = - 2

into

x^{3} - 9 x^{2} - 48 x : 52

Maximum (- 2, 52)

Plug

x = 8

into

x^{3} - 9 x^{2} - 48 x : - 448

Minimum (8, - 448)

Maximum (- 2, 52), Minimum (8, - 448)

f (x, y) = 100 (y - x^{2})^{2} + (1 - x)^{2}

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

\frac{x ^{2}}{x ^{2} + 2 x - 15}

f (x, y) = - x^{2} + 5 y^{2} + 10 x - 10 y - 28

y = (x - 2)^{2} (x + 4)

What is the extreme y=x^3-9x^2-48x ?
The extreme y=x^3-9x^2-48x is Maximum(-2,52),Minimum(8,-448)