Find the absolute maximum and absolute minimum value of fx

Find the absolute maximum and absolute minimum value of f(x) = 3x4 - 4x3 - 8 on the interval - 1 x 2. Find the absolute maximum and absolute minimum values of f(x) = cos x + sin x on the interval 0 x 2 pi.

Solution

a) f\' = 12x^3-12x^2 for maxima or minima, f\' =0 12x^3-12x^2 = 0 x = 0,1 values at f(-1) = -1 f(0) = -8 f(1) = -9 f(2)=8 so maxima at x =2 and minima at x=1 b) f\' = cos x- sin x f\'=0 x = pi / 4 , 3*pi/4 values at f(0) = 1 f(pi/4) =1.414 f(3*pi/4) = -1.414 f(2pi)=1 so maxima at x =pi/4 and minima at x=3pi/4