What is the extreme f(x)= 10/3 x^3+13x^2+12x+50 ?

The extreme f(x)= 10/3 x^3+13x^2+12x+50 is Maximum(-2, 154/3),Minimum(-3/5 , 1169/25)

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extreme f(x)= 10/3 x^3+13x^2+12x+50

extreme points

f (x) = \frac{10}{3} x^{3} + 13 x^{2} + 12 x + 50

Maximum (- 2, \frac{154}{3}), Minimum (- \frac{3}{5}, \frac{1169}{25})

Solution steps

f^{'} (x) = 10 x^{2} + 26 x + 12

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < - \frac{3}{5},

Increasing

: - \frac{3}{5} < x < \infty

Plug

x = - 2

into

\frac{10}{3} x^{3} + 13 x^{2} + 12 x + 50 : \frac{154}{3}

Maximum (- 2, \frac{154}{3})

Plug

x = - \frac{3}{5}

into

\frac{10}{3} x^{3} + 13 x^{2} + 12 x + 50 : \frac{1169}{25}

Minimum (- \frac{3}{5}, \frac{1169}{25})

Maximum (- 2, \frac{154}{3}), Minimum (- \frac{3}{5}, \frac{1169}{25})

9 - 2 x + 4 y - x^{2} - 4 y^{2}

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

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

f (x) = - 5 cos (x - 3 π)

f (x) = \frac{- 5}{x ^{2} - 4}

What is the extreme f(x)= 10/3 x^3+13x^2+12x+50 ?
The extreme f(x)= 10/3 x^3+13x^2+12x+50 is Maximum(-2, 154/3),Minimum(-3/5 , 1169/25)