How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for f(x) = x² + 2x - 3?

1 Answer
Bill K.
Feb 5, 2016

Use the derivative. The function is (strictly) increasing over intervals where f'(x) > 0 and (strictly) decreasing over intervals where f'(x) < 0. Local extreme points occur at critical points where f'(x) = 0 or where f'(x) is undefined.

Explanation:

If f(x)=x^2+2x-3, then f'(x)=2x+2 so that f'(x) < 0 when x < -1 and f'(x) > 0 when x > -1. This means f is decreasing over the interval x <= -1 and f is increasing over the interval x >= -1. f has a local minimum value at the critical point x=-1 equal to f(-1)=1-2-3=-4.

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