What is the extreme f(x)=x^3+5x^2-8x+1 ?

The extreme f(x)=x^3+5x^2-8x+1 is Maximum(-4,49),Minimum(2/3 ,-49/27)

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extreme f(x)=x^3+5x^2-8x+1

extreme points

f (x) = x^{3} + 5 x^{2} - 8 x + 1

Maximum (- 4, 49), Minimum (\frac{2}{3}, - \frac{49}{27})

Solution steps

f^{'} (x) = 3 x^{2} + 10 x - 8

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

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

Increasing

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

Plug

x = - 4

into

x^{3} + 5 x^{2} - 8 x + 1 : 49

Maximum (- 4, 49)

Plug

x = \frac{2}{3}

into

x^{3} + 5 x^{2} - 8 x + 1 : - \frac{49}{27}

Minimum (\frac{2}{3}, - \frac{49}{27})

Maximum (- 4, 49), Minimum (\frac{2}{3}, - \frac{49}{27})

f (x) = 7 x^{\frac{8}{3}}

\frac{6}{x} + \frac{3}{y} + 14 x + 5 y

y = x - sin (- x), 0 \leq x \leq 2 π

x^{2} (2 - x)^{3}

f (x, y) = 2 x^{2} - 5 y^{2} + 6 y

What is the extreme f(x)=x^3+5x^2-8x+1 ?
The extreme f(x)=x^3+5x^2-8x+1 is Maximum(-4,49),Minimum(2/3 ,-49/27)