Complete the square to determine the maximum or minimum value of the function defined by the expression - x2-10x+14

maximum value = 39

Step-by-step explanation:

Since the coefficient of the x² term < 0 then function has a maximum value

to complete the square the coefficient of the x² term must be 1

factor out - 1

- (x² + 10x - 14)

add/subtract (half the coefficient of the x - term) ² to x² + 10x

= - (x² + 2 (5) x + 25 - 25 - 14)

= - (x + 5) ² + 39

The maximum occurs when x = - 5 ⇒ max = 39

Maximum value of the function = 39.

Step-by-step explanation:

It will have a maximum value because the coefficient of x^2 is negative.

-x2 - 10x + 14

= - (x^2 + 10x) + 14

Completing the square:

= - [ (x + 5) ^2 - 25) ] + 14

Maximum value = - (-25) + 14

= 39 (answer).

Value of x at the maximum = - 5.