What is the extreme f(x)=4x^3-39x^2+90x+2 ?

The extreme f(x)=4x^3-39x^2+90x+2 is Maximum(3/2 , 251/4),Minimum(5,-23)

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extreme f(x)=4x^3-39x^2+90x+2

extreme points

f (x) = 4 x^{3} - 39 x^{2} + 90 x + 2

Maximum (\frac{3}{2}, \frac{251}{4}), Minimum (5, - 23)

Solution steps

f^{'} (x) = 12 x^{2} - 78 x + 90

Find intervals:

Increasing

: - \infty < x < \frac{3}{2},

Decreasing

: \frac{3}{2} < x < 5,

Increasing

: 5 < x < \infty

Plug

x = \frac{3}{2}

into

4 x^{3} - 39 x^{2} + 90 x + 2 : \frac{251}{4}

Maximum (\frac{3}{2}, \frac{251}{4})

Plug

x = 5

into

4 x^{3} - 39 x^{2} + 90 x + 2 : - 23

Minimum (5, - 23)

Maximum (\frac{3}{2}, \frac{251}{4}), Minimum (5, - 23)

What is the extreme f(x)=4x^3-39x^2+90x+2 ?
The extreme f(x)=4x^3-39x^2+90x+2 is Maximum(3/2 , 251/4),Minimum(5,-23)