Problem+27+Sam+O+and+Sam+B

Sketch the graph

27. f’(x)>0 if |x|<2, f’(x)<0 if |x|>2, f’(-2)= 0, lim x→2|f’(x)|= ∞, f"(x)>0 if x≠2

The function is increasing, when -22 There is a critical point at x=-2, this point is a local min, (if the graph has a cusp then there is a local max at x=2) Except at 2, the function is concave up Since the limit of derivative of the function as x approaches 2 is infinite, at x=2 there is either a vertical asymptote at x=2, where on both sides the function goes to infinite (can't go down, because the function is concave up), or there is a cusp.

Could not agree more...

This is what the graph (the one with the asymptote) could look like...the little horizontal line at x=-2 represents the horizontal tangent line