What is the extreme x^3-6x^2-15x+2 ?

The extreme x^3-6x^2-15x+2 is Maximum(-1,10),Minimum(5,-98)

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extreme x^3-6x^2-15x+2

extreme points

x^{3} - 6 x^{2} - 15 x + 2

Maximum (- 1, 10), Minimum (5, - 98)

Solution steps

f^{'} (x) = 3 x^{2} - 12 x - 15

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = - 1

into

x^{3} - 6 x^{2} - 15 x + 2 : 10

Maximum (- 1, 10)

Plug

x = 5

into

x^{3} - 6 x^{2} - 15 x + 2 : - 98

Minimum (5, - 98)

Maximum (- 1, 10), Minimum (5, - 98)

x^{3} - 6 x^{2} - 15 x + 4

x^{3} - 6 x^{2} - 15 x + 6

f (x, y) = x^{2} + 2 y^{2} + 3 x + 10

x^{4} - 128 x^{2} + 9

f (x) = 2 x^{3} - 33 x^{2} + 144 x + 3, (4, 9)

What is the extreme x^3-6x^2-15x+2 ?
The extreme x^3-6x^2-15x+2 is Maximum(-1,10),Minimum(5,-98)