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

The extreme f(x)=-x^3+5x^2+8x-3 is Minimum(-2/3 ,-157/27),Maximum(4,45)

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

extreme points

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

Minimum (- \frac{2}{3}, - \frac{157}{27}), Maximum (4, 45)

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Decreasing

: 4 < x < \infty

Plug

x = - \frac{2}{3}

into

- x^{3} + 5 x^{2} + 8 x - 3 : - \frac{157}{27}

Minimum (- \frac{2}{3}, - \frac{157}{27})

Plug

x = 4

into

- x^{3} + 5 x^{2} + 8 x - 3 : 45

Maximum (4, 45)

Minimum (- \frac{2}{3}, - \frac{157}{27}), Maximum (4, 45)

f (x) = 3^{x} - 5

cos (3 x)

y - 70.75 = 0.11 (x - 250)

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

(5, 2), (- 6, - 3)

What is the extreme f(x)=-x^3+5x^2+8x-3 ?
The extreme f(x)=-x^3+5x^2+8x-3 is Minimum(-2/3 ,-157/27),Maximum(4,45)