Determine the extreme value of the function h(x) = 5x-3x^2

Expert Answers

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Given the function: h(x) = 5x-3x^2

We need to find the extreme values for h(x)

First, we need to find the first derivative h'(x).

==> h'(x) = 5 - 6x

Now we will determine the derivatives zero.

==> 5 - 6x = 0

==> x = 5/6

Then, the function h(x) has an extreme values when x = 5/6

==> h(5/6) = 5(5/6) - 3(5/6)^2

                  = 25/6 - 3(25/36

                    = 25/6 - 75/36 = 75/36  = 25/12

==> h(5/6) = 25/12

We also notice that the sign of x^2 is negative.

Then, the function has maximum values at the point ( 5/6, 25/12)

Or at h(5/6) = 25/12

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