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.

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step-by-step explanation:

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40