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

The extreme f(x)=2x^3-9x^2+3,-2<= x<= 2 is Minimum(-2,-49),Maximum(0,3),Minimum(2,-17)

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

extreme points

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

Minimum (- 2, - 49), Maximum (0, 3), Minimum (2, - 17)

Solution steps

Find the critical points:

x = - 2, x = 0, x = 2

Domain of

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

Find intervals:

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2

Plug the extreme point

x = - 2

into

2 x^{3} - 9 x^{2} + 3 \Rightarrow y = - 49

Minimum (- 2, - 49)

Plug the extreme point

x = 0

into

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

Maximum (0, 3)

Plug the extreme point

x = 2

into

2 x^{3} - 9 x^{2} + 3 \Rightarrow y = - 17

Minimum (2, - 17)

Minimum (- 2, - 49), Maximum (0, 3), Minimum (2, - 17)

f (x, y) = x^{3} + y^{3} + 3 x y^{2} - 18 x - 18 y

f (x) = 2 x^{4} - 36 x^{2}

f (x) = 25 (x^{2} - y^{2}) - 2 (x^{2} + y^{2})^{2}

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

f (x, y) = 80 x^{\frac{4}{10}} y^{\frac{2}{10}}

What is the extreme f(x)=2x^3-9x^2+3,-2<= x<= 2 ?
The extreme f(x)=2x^3-9x^2+3,-2<= x<= 2 is Minimum(-2,-49),Maximum(0,3),Minimum(2,-17)