What is the extreme f(x)=8x^3-17x^2+12x+14 ?

The extreme f(x)=8x^3-17x^2+12x+14 is Maximum(2/3 , 454/27),Minimum(3/4 , 269/16)

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extreme f(x)=8x^3-17x^2+12x+14

extreme points

f (x) = 8 x^{3} - 17 x^{2} + 12 x + 14

Maximum (\frac{2}{3}, \frac{454}{27}), Minimum (\frac{3}{4}, \frac{269}{16})

Solution steps

f^{'} (x) = 24 x^{2} - 34 x + 12

Find intervals:

Increasing

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

Decreasing

: \frac{2}{3} < x < \frac{3}{4},

Increasing

: \frac{3}{4} < x < \infty

Plug

x = \frac{2}{3}

into

8 x^{3} - 17 x^{2} + 12 x + 14 : \frac{454}{27}

Maximum (\frac{2}{3}, \frac{454}{27})

Plug

x = \frac{3}{4}

into

8 x^{3} - 17 x^{2} + 12 x + 14 : \frac{269}{16}

Minimum (\frac{3}{4}, \frac{269}{16})

Maximum (\frac{2}{3}, \frac{454}{27}), Minimum (\frac{3}{4}, \frac{269}{16})

f (x, y) = 3 y^{3} + 7 x y - 9 x^{2} - 5

f (x) = - \frac{cos ( 2 x )}{2} - 2 sin (x)

f (x) = e^{x^{2} - 4 x - 1}

y = e^{x} + I n x - x^{2} + \frac{3}{x ^{5}} + 3

f (x) = ln (1 + x^{2})

What is the extreme f(x)=8x^3-17x^2+12x+14 ?
The extreme f(x)=8x^3-17x^2+12x+14 is Maximum(2/3 , 454/27),Minimum(3/4 , 269/16)