What is the extreme f(x)=2x^3-15x^2+36x+10 ?

The extreme f(x)=2x^3-15x^2+36x+10 is Maximum(2,38),Minimum(3,37)

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extreme f(x)=2x^3-15x^2+36x+10

extreme points

f (x) = 2 x^{3} - 15 x^{2} + 36 x + 10

Maximum (2, 38), Minimum (3, 37)

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 + 10 : 38

Maximum (2, 38)

Plug

x = 3

into

2 x^{3} - 15 x^{2} + 36 x + 10 : 37

Minimum (3, 37)

Maximum (2, 38), Minimum (3, 37)

f (x) = x^{3} - 12 x^{2} + 45 x + 5

f (x) = - x^{\frac{5}{3}} + 5 3 x

f (x) = e^{- a x}

f (x) = - x^{3} + 6 x^{2} - 9 x

f (x) = x^{2} + 9 x + 5

What is the extreme f(x)=2x^3-15x^2+36x+10 ?
The extreme f(x)=2x^3-15x^2+36x+10 is Maximum(2,38),Minimum(3,37)