What is the extreme f(x)=x^3-2x^2-15x+5,-2<= x<= 0 ?

The extreme f(x)=x^3-2x^2-15x+5,-2<= x<= 0 is Minimum(-2,19),Maximum(-5/3 , 535/27),Minimum(0,5)

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extreme f(x)=x^3-2x^2-15x+5,-2<= x<= 0

extreme points

f (x) = x^{3} - 2 x^{2} - 15 x + 5, - 2 \leq x \leq 0

Minimum (- 2, 19), Maximum (- \frac{5}{3}, \frac{535}{27}), Minimum (0, 5)

Solution steps

Find the critical points:

x = - 2, x = - \frac{5}{3}, x = 0

Domain of

x^{3} - 2 x^{2} - 15 x + 5, - 2 \leq x \leq 0 : - 2 \leq x \leq 0

Find intervals:

Increasing

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

Decreasing

: - \frac{5}{3} < x < 0

Plug the extreme point

x = - 2

into

x^{3} - 2 x^{2} - 15 x + 5 \Rightarrow y = 19

Minimum (- 2, 19)

Plug the extreme point

x = - \frac{5}{3}

into

x^{3} - 2 x^{2} - 15 x + 5 \Rightarrow y = \frac{535}{27}

Maximum (- \frac{5}{3}, \frac{535}{27})

Plug the extreme point

x = 0

into

x^{3} - 2 x^{2} - 15 x + 5 \Rightarrow y = 5

Minimum (0, 5)

Minimum (- 2, 19), Maximum (- \frac{5}{3}, \frac{535}{27}), Minimum (0, 5)

x^{2} (x - 18) + 96 x + 2000

f (x, y) = y x + 4 x y + 2 y + 12

f (x) = - 20 x^{2} - 70 x + 120

\frac{x}{e ^{x}}

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

What is the extreme f(x)=x^3-2x^2-15x+5,-2<= x<= 0 ?
The extreme f(x)=x^3-2x^2-15x+5,-2<= x<= 0 is Minimum(-2,19),Maximum(-5/3 , 535/27),Minimum(0,5)