What is the extreme f(x)=(x^3)/3-4x^2+7x+8 ?

The extreme f(x)=(x^3)/3-4x^2+7x+8 is Maximum(1, 34/3),Minimum(7,-74/3)

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extreme f(x)=(x^3)/3-4x^2+7x+8

extreme points

f (x) = \frac{x ^{3}}{3} - 4 x^{2} + 7 x + 8

Maximum (1, \frac{34}{3}), Minimum (7, - \frac{74}{3})

Solution steps

f^{'} (x) = x^{2} - 8 x + 7

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 7,

Increasing

: 7 < x < \infty

Plug

x = 1

into

\frac{x ^{3}}{3} - 4 x^{2} + 7 x + 8 : \frac{34}{3}

Maximum (1, \frac{34}{3})

Plug

x = 7

into

\frac{x ^{3}}{3} - 4 x^{2} + 7 x + 8 : - \frac{74}{3}

Minimum (7, - \frac{74}{3})

Maximum (1, \frac{34}{3}), Minimum (7, - \frac{74}{3})

F (x, y) = - x^{3} + 6 x y - 3 y^{2} + 1

f (x y) = x^{3} + 3 y^{3} + 3 x^{2} + 3 y^{2} + 24

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

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

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

What is the extreme f(x)=(x^3)/3-4x^2+7x+8 ?
The extreme f(x)=(x^3)/3-4x^2+7x+8 is Maximum(1, 34/3),Minimum(7,-74/3)