Math, asked by rajchaudhari20p55p6f, 11 months ago

Find the maximum and minimum values of x³-3x+11

Answers

Answered by MaheswariS
2

Answer:

Maximum value =13

Minimum value = 9

Step-by-step explanation:

Let f(x)=x^3-3x+11

f '(x)=3x^2-3

f ''(x)=6x

Now,

f '(x)=0

\implies\:3(x^2-1)=0

\implies\:x^2-1=0

\implies\:x^2=1

\implies\:x=1,-1

At x=1, f ''(x)=6(1)=6>0

\therefore f attaains minimum at x=1

Minimum value =f(1)=1^3-3(1)+11=1-3+11=12-3=9

At x=-1, f ''(x)=6(-1)=-6<0

\therefore f attaains maximum at x=-1

Maximum value =f(1)=(-1)^3-3(-1)+11=-1+3+11=13

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