f(x) = –2x2 + 8x + 3

Question

determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value.

Answer 1

f(x) = -2x^2 + 8x + 3

Since the number in front of x^2 is negative this means the function has a maximum value.

The to find the point where it reaches a maximum, differentiate the function.

f '(x) = -4x + 8

Stationary points when f' (x) = 0

so -4x + 8 = 0

-4x = -8

-x = -2

x = 2

Then put x = 2 into original equation to find the value of y,

y = -2 x 2^2 + 8 x 2 + 3 = 11

So the maximum value is at (2,11)