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 answer: the function is increasing at (-inf, 7) the function is decreasing at [7, inf)
