Answer the questions below about the quadratic function.

User Generated

cgureevna

Mathematics

Description

g(x)= -3x^2 - 18x - 25

a.) Does the funtion have a maximum or minimum value?

b.) Where does the minimum or maximum value occur?

c.) What is the functions minimum or maximum value? 

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Explanation & Answer

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g(x)= -3x^2 - 18x - 25

a.

To determine whether the function has a minimum or maximum point, we differentiate the function twice.

Therefore, g'(x) = -6x-18

                 g"(x) = -6

The function has a maximum point since the second derivative is negative.

b.

The maximum point is at the point where the gradient of the function is zero, represented by the first derivative.

0 = -6x-18

6x=18

x= 3

The maximum point is at the point where x=3

c.

To obtain the maximum value, we substitute x=3 to the function:-

g(x) =-3(3^2)-18(3)-25

        =-27-54-25

      = -106

The functions maximum value is -106


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