What is the extreme f(x)=2x^3-15x^2+24x ?

The extreme f(x)=2x^3-15x^2+24x is Maximum(1,11),Minimum(4,-16)

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extreme f(x)=2x^3-15x^2+24x

extreme points

f (x) = 2 x^{3} - 15 x^{2} + 24 x

Maximum (1, 11), Minimum (4, - 16)

Solution steps

f^{'} (x) = 6 x^{2} - 30 x + 24

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 1

into

2 x^{3} - 15 x^{2} + 24 x : 11

Maximum (1, 11)

Plug

x = 4

into

2 x^{3} - 15 x^{2} + 24 x : - 16

Minimum (4, - 16)

Maximum (1, 11), Minimum (4, - 16)

What is the extreme f(x)=2x^3-15x^2+24x ?
The extreme f(x)=2x^3-15x^2+24x is Maximum(1,11),Minimum(4,-16)