What is the minimum values of the function v(x) = 3x^2 -3x +5 ?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

To find the minimum value of v(x) = 3x^2 -3x +5, we find the derivative and equate that to zero

v(x) = 3x^2 -3x +5

=> v'(x) = 6x - 3

6x - 3 = 0

=> x = 3/6 = 1/2

For x = 1/2 , v(x) = 3*(1/2)^2 - 3*(1/2) + 5

=> 3*1/4 - 3/2 + 5

=> 3/4 - 3/2 + 5

=> 4.25

Also v''(x) = 6 which is positive for x= 1/2

Therefore the minimum value of the function is 4.25

Approved by eNotes Editorial Team
An illustration of the letter 'A' in a speech bubbles

Given the function:

v(x) = 3x^2 - 3x + 5

We need to find the minimum values of v(x).

First we will determine the first derivative v'(x).

==> v'(x) = 6x -3

Now we will calculate the derivatives zero.

==> 6x -3 = 0 ==> 6x = 3 ==> x = 1/2

Then, the critical value for v(x) is the point x = 1/2

Now we will find the values of v(1/2).

==> v(1/2) = 3(1/2)^2 - 3(1/2) +5

                   = 3/4 - 3/2 + 5 = (3 - 6 + 20)/4 = 17/4

==> The minimum value of the function v(x) is the point (1/2, 17/4)

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial