What is the extreme f(x)=x^3+3x^2+9,0<= x<= 10 ?

The extreme f(x)=x^3+3x^2+9,0<= x<= 10 is Minimum(0,9),Maximum(10,1309)

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extreme f(x)=x^3+3x^2+9,0<= x<= 10

extreme

Minimum (0, 9), Maximum (10, 1309)

Solution steps

Find the critical points:

x = 0, x = 10

Domain of

x^{3} + 3 x^{2} + 9, 0 \leq x \leq 10 : 0 \leq x \leq 10

Find intervals:

Increasing

: 0 < x < 10

Plug the extreme point

x = 0

into

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

Minimum (0, 9)

Plug the extreme point

x = 10

into

x^{3} + 3 x^{2} + 9 \Rightarrow y = 1309

Maximum (10, 1309)

Minimum (0, 9), Maximum (10, 1309)

What is the extreme f(x)=x^3+3x^2+9,0<= x<= 10 ?
The extreme f(x)=x^3+3x^2+9,0<= x<= 10 is Minimum(0,9),Maximum(10,1309)