Question

Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals:

f (x) x²,x€[-2,2]

Answer 1

(i) The given function is f(x) = x³.

Then, we evaluate the value of f at critical point x = 0 and at end points of the interval [−2, 2]. f(0) = 0 f(−2) = (−2)³ = −8 f(2) = (2)³ = 8

Hence, we can conclude that the absolute maximum value of f on [−2, 2] is 8 occurring at x = 2. Also, the absolute minimum value of f on [−2, 2] is −8 occurring at x = −2.