What is the extreme f(x)=4x^3-39x^2+90x-6 ?

The extreme f(x)=4x^3-39x^2+90x-6 is Maximum(3/2 , 219/4),Minimum(5,-31)

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extreme f(x)=4x^3-39x^2+90x-6

extreme

Maximum (\frac{3}{2}, \frac{219}{4}), Minimum (5, - 31)

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 - 6 : \frac{219}{4}

Maximum (\frac{3}{2}, \frac{219}{4})

Plug

x = 5

into

4 x^{3} - 39 x^{2} + 90 x - 6 : - 31

Minimum (5, - 31)

Maximum (\frac{3}{2}, \frac{219}{4}), Minimum (5, - 31)

What is the extreme f(x)=4x^3-39x^2+90x-6 ?
The extreme f(x)=4x^3-39x^2+90x-6 is Maximum(3/2 , 219/4),Minimum(5,-31)