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

The extreme f(x)=4x^3-x^2-4x+3 is Maximum(-1/2 , 17/4),Minimum(2/3 , 29/27)

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

extreme points

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

Maximum (- \frac{1}{2}, \frac{17}{4}), Minimum (\frac{2}{3}, \frac{29}{27})

Solution steps

f^{'} (x) = 12 x^{2} - 2 x - 4

Find intervals:

Increasing

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

Decreasing

: - \frac{1}{2} < x < \frac{2}{3},

Increasing

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

Plug

x = - \frac{1}{2}

into

4 x^{3} - x^{2} - 4 x + 3 : \frac{17}{4}

Maximum (- \frac{1}{2}, \frac{17}{4})

Plug

x = \frac{2}{3}

into

4 x^{3} - x^{2} - 4 x + 3 : \frac{29}{27}

Minimum (\frac{2}{3}, \frac{29}{27})

Maximum (- \frac{1}{2}, \frac{17}{4}), Minimum (\frac{2}{3}, \frac{29}{27})

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

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

f (x, y) = e^{x} ln (y)

f (x) = 3 x^{4} - 4 x^{3}, - 1 \leq x \leq 2

f (x) = x^{3} + 45 x^{2} + 87 x + 28

What is the extreme f(x)=4x^3-x^2-4x+3 ?
The extreme f(x)=4x^3-x^2-4x+3 is Maximum(-1/2 , 17/4),Minimum(2/3 , 29/27)