The absolute minimum value of f(x)=(x^{3}/3)-(5x^{2}/2)-6x on [-1,3] is?

Monique Slaughter 2021-12-13 Answered
The absolute minimum value of f(x)=(x33)(5x22)6x on [-1,3] is?
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

chumants6g
Answered 2021-12-14 Author has 33 answers

Given,
f(x)=x335x226x,[1,3]
Differentiating with respect to x, we get
f(x)=13(3x2)52(2x)6(1)
=x25x6
Now to find critical values, solve the first derivative by equating it to zero. That is,
f'(x)=0
x25x6=0
x26x+x6=0
x(x6)+(x6)=0
(x6)(x=1)=0
x=6 or x=1
But 6 not  [-1,3], therefore critical value is x=-1.
Step 2
Now we find the value of the function at the critical value and at the end points of the given interval.
When x=-1,
f(1)=(1)335(1)226(1)
=1352+6
=215+366
=196
When x=3,
f(3)=(3)335(3)226(3)
=945218
=1845362
=632
Hence absolute minimum value is 632 which occurs at x=3.

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