What is the extreme f(x)=2x^3+9x^2-60x+6,-5<= x<= 5 ?

The extreme f(x)=2x^3+9x^2-60x+6,-5<= x<= 5 is Maximum(-5,281),Minimum(2,-62),Maximum(5,181)

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extreme f(x)=2x^3+9x^2-60x+6,-5<= x<= 5

extreme points

f (x) = 2 x^{3} + 9 x^{2} - 60 x + 6, - 5 \leq x \leq 5

Maximum (- 5, 281), Minimum (2, - 62), Maximum (5, 181)

Solution steps

Find the critical points:

x = - 5, x = 2, x = 5

Domain of

2 x^{3} + 9 x^{2} - 60 x + 6, - 5 \leq x \leq 5 : - 5 \leq x \leq 5

Find intervals:

Decreasing

: - 5 < x < 2,

Increasing

: 2 < x < 5

Plug the extreme point

x = - 5

into

2 x^{3} + 9 x^{2} - 60 x + 6 \Rightarrow y = 281

Maximum (- 5, 281)

Plug the extreme point

x = 2

into

2 x^{3} + 9 x^{2} - 60 x + 6 \Rightarrow y = - 62

Minimum (2, - 62)

Plug the extreme point

x = 5

into

2 x^{3} + 9 x^{2} - 60 x + 6 \Rightarrow y = 181

Maximum (5, 181)

Maximum (- 5, 281), Minimum (2, - 62), Maximum (5, 181)

f (x) = x^{\frac{1}{7}}

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

f (x) = x^{4} - 108 x

f (x, y) = 11 x^{2} - 2 x y + 2 y^{2} + 3

What is the extreme f(x)=2x^3+9x^2-60x+6,-5<= x<= 5 ?
The extreme f(x)=2x^3+9x^2-60x+6,-5<= x<= 5 is Maximum(-5,281),Minimum(2,-62),Maximum(5,181)