In each of 1 through 10, write the Fourier integral representation (14.1) of the function and determine what this integral converges to.f (x) = |x| for x 2 0 for x < and for x > 2

Calculus notes for the week of 10/3/16 4.1 Maxima and Minima and 4.2 What Derivatives Tell Us 15 10 5 01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 -5 -10 -15 f has a local maximum at c if f(c) > f(x) for all x sufficiently close to c. f has a local minimum at c if f(c) < f(x) for all x sufficiently close to c. We see that, if f is differentiable at a local extremum (c), then f’(c) = 0. It is impossible that f is not differentiable at a local extremum. Definition: f has a critical point at x if f ’(x) = 0 or f ’(x) DNE. Coordinates for local extremum will be critical points. We see that, if f ‘(x) is negative on an interval I, then f is decreasing on I. If f ‘(x) is positive on an interval I, then f is