What is the extreme f(x)=2x^3-15x^2+36x ?

The extreme f(x)=2x^3-15x^2+36x is Maximum(2,28),Minimum(3,27)

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extreme f(x)=2x^3-15x^2+36x

extreme points

f (x) = 2 x^{3} - 15 x^{2} + 36 x

Maximum (2, 28), Minimum (3, 27)

Solution steps

f^{'} (x) = 6 x^{2} - 30 x + 36

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 2

into

2 x^{3} - 15 x^{2} + 36 x : 28

Maximum (2, 28)

Plug

x = 3

into

2 x^{3} - 15 x^{2} + 36 x : 27

Minimum (3, 27)

Maximum (2, 28), Minimum (3, 27)

f (x, y) = 60 x + 30 y - 2 x^{2} - 3 y^{2}

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

f (x, y) = \frac{( x ^{2} + y ^{2} - 1 )}{4}

y = 2 x^{3} - 33 x^{2} + 168 x - 8

What is the extreme f(x)=2x^3-15x^2+36x ?
The extreme f(x)=2x^3-15x^2+36x is Maximum(2,28),Minimum(3,27)