Cracking The Ap Calculus ab Exam 2018

First, note that the derivative is zero at the point (0, 1) because the tangent line is horizontal there. Next,
the derivative is negative for all x < 0 because the tangent lines to the curve have negative slopes
everywhere on the interval (−∞, 0). Finally, the derivative is positive for all x > 0 because the tangent
lines to the curve have positive slopes everywhere on the interval (0, ∞). Now we can make a graph of
the derivative. It will go through the origin (because the derivative is 0 at x = 0), it will be negative on the
interval (−∞, 0) and it will be positive on the interval (0, ∞). The graph looks something like the
following: