Find the absolute extrema of f(x)=7x^{\frac{1}{3}}-x^{\frac{7}{3}} over the interval [-8,8].

Walter Clyburn 2021-12-06 Answered
Find the absolute extrema of f(x)=7x13x73 over the interval [-8,8].
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Annie Levasseur
Answered 2021-12-07 Author has 30 answers
Step 1
Given function is
f(x)=7x13x73
f(x)=73x13173x731
f(x)=73x2373x43
f(x)=73(1x23x43)=73(1x43x23x23)=73(1x2x23)
Step 2
Now, we solve f'(x)=0 for x
f'(x)=0
1x2x23=0
1x2=0
x=±1
Also. f'(x) is not defined for x=0, so all critical numbers of f(x) are -1,0,1
Step 3
Now, we find value of f at the end-points of interval and critical points
f(x)=7x13x73
f(8)=7(8)13(8)73=7(2)(2)7=114
f(1)=7(1)13(1)73=7(1)(1)7=6
f(0)=7(0)13(0)73=0
f(1)=7(1)13(1)73=7(1)(1)7=6
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions