Question

Identify intervals on which the function is increasing, decreasing, or constant.

g(x) = 2 - (x - 7)2

Increasing: x < 2; decreasing: x > 2

Increasing: x < -7; decreasing: x > -7

Increasing: x < 7; decreasing: x > 7

Increasing: x > 2; decreasing: x < 2

Answer 1

g ( x ) = 2 - ( x - 7 )²
g ( x ) = 2 - ( x² - 14 x + 49 )
g ( x ) = 2 - x² + 14 x - 49
g ( x ) = - x² + 14 x - 47
The maximum of the function is at:
x= - b / 2 a
x = - 14 / ( - 2 ) = 7
Therefore the function is increasing form x ∈ ( - ∞, 7 ) and decreasing for x ∈ ( 7, +∞ ).
Answer:
C. increasing, x < 7; decreasing x > 7.