What is the extreme f(x)=-3x^3-63/2 x^2-90x+1 ?

The extreme f(x)=-3x^3-63/2 x^2-90x+1 is Minimum(-5, 77/2),Maximum(-2,79)

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extreme f(x)=-3x^3-63/2 x^2-90x+1

extreme points

f (x) = - 3 x^{3} - \frac{63}{2} x^{2} - 90 x + 1

Minimum (- 5, \frac{77}{2}), Maximum (- 2, 79)

Solution steps

f^{'} (x) = - 9 x^{2} - 63 x - 90

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < - 2,

Decreasing

: - 2 < x < \infty

Plug

x = - 5

into

- 3 x^{3} - \frac{63}{2} x^{2} - 90 x + 1 : \frac{77}{2}

Minimum (- 5, \frac{77}{2})

Plug

x = - 2

into

- 3 x^{3} - \frac{63}{2} x^{2} - 90 x + 1 : 79

Maximum (- 2, 79)

Minimum (- 5, \frac{77}{2}), Maximum (- 2, 79)

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

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

f (x) = \frac{x + 4}{x ^{2} - 3 x - 28}

f (x) = 2 + 9 x + 3 x^{2} - x^{3}

f (x) = cos (x) - 2 x

What is the extreme f(x)=-3x^3-63/2 x^2-90x+1 ?
The extreme f(x)=-3x^3-63/2 x^2-90x+1 is Minimum(-5, 77/2),Maximum(-2,79)