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

The extreme f(x)=4x^3-3x^2-6x is Maximum(-1/2 , 7/4),Minimum(1,-5)

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

extreme points

f (x) = 4 x^{3} - 3 x^{2} - 6 x

Maximum (- \frac{1}{2}, \frac{7}{4}), Minimum (1, - 5)

Solution steps

f^{'} (x) = 12 x^{2} - 6 x - 6

Find intervals:

Increasing

: - \infty < x < - \frac{1}{2},

Decreasing

: - \frac{1}{2} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - \frac{1}{2}

into

4 x^{3} - 3 x^{2} - 6 x : \frac{7}{4}

Maximum (- \frac{1}{2}, \frac{7}{4})

Plug

x = 1

into

4 x^{3} - 3 x^{2} - 6 x : - 5

Minimum (1, - 5)

Maximum (- \frac{1}{2}, \frac{7}{4}), Minimum (1, - 5)

f (x) = - \frac{3}{4} x + 2

7 x - 4

6 + x - 2 x^{2}

f (x) = x^{4} - 32 x + 9

f (x) = \frac{1}{4} cos (\frac{8 π x}{3})

What is the extreme f(x)=4x^3-3x^2-6x ?
The extreme f(x)=4x^3-3x^2-6x is Maximum(-1/2 , 7/4),Minimum(1,-5)