Respuesta :
Answer:
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
Answer:
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.
