Identify intervals on which the function is increasing, decreasing, or constant. g(x)= 1-(x-7)^2

Calculation of relative maxima and minima of a function f (x) in a range [a, b]:
 We find the first derivative and calculate its roots.
 We make the second derivative, and calculate the sign taken in it by the roots of the first derivative, and if:
 f '' (a) <0 is a relative maximum
 f '' (a)> 0 is a relative minimum
 Identify intervals on which the function is increasing, decreasing, or constant. G (x) = 1- (x-7) ^ 2
 First derivative
 G '(x) = - 2 (x-7)
 -2 (x-7) = 0
 x = 7
 Second derivative
 G '' (x) = - 2
 G '' (7) = - 2 <0 is a relative maximum
 
 the function is increasing at (-inf, 7)
 the function is decreasing at [7, inf)