What is the extreme 3x^3+30x^2+75x-9 ?

The extreme 3x^3+30x^2+75x-9 is Maximum(-5,-9),Minimum(-5/3 ,-581/9)

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extreme 3x^3+30x^2+75x-9

extreme points

3 x^{3} + 30 x^{2} + 75 x - 9

Maximum (- 5, - 9), Minimum (- \frac{5}{3}, - \frac{581}{9})

Solution steps

f^{'} (x) = 9 x^{2} + 60 x + 75

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

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

Increasing

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

Plug

x = - 5

into

3 x^{3} + 30 x^{2} + 75 x - 9 : - 9

Maximum (- 5, - 9)

Plug

x = - \frac{5}{3}

into

3 x^{3} + 30 x^{2} + 75 x - 9 : - \frac{581}{9}

Minimum (- \frac{5}{3}, - \frac{581}{9})

Maximum (- 5, - 9), Minimum (- \frac{5}{3}, - \frac{581}{9})

f (x) = 2 x + 3200

f (x) = 2 x + \frac{8}{x ^{2}} + 1, x > 0

f (x) = \frac{1}{x ^{2}} + \frac{1}{x ^{3}}

f (x, y) = x^{3} + y^{3} - 63 (x + y) + 12 x y

f (x, y) = x^{2} + 3 y^{2} - 4 x + 6 y

What is the extreme 3x^3+30x^2+75x-9 ?
The extreme 3x^3+30x^2+75x-9 is Maximum(-5,-9),Minimum(-5/3 ,-581/9)