Cracking the AP Calculus AB & BC Exams, 2014 Edition by Princeton Review

Author:Princeton Review [Review, The Princeton]
Language: eng
Format: epub
ISBN: 978-0-307-94619-5
Publisher: Random House Information Group
Published: 2013-09-16T16:00:00+00:00

5. Vertical asymptote at x = –8; Horizontal asymptote at y = 1; No maxima, minima, or points of inflection.

First, notice that there is an x-intercept at x = 3 and that the y-intercept is . Next, we take the derivative: . Next we set the derivative equal to zero to find the critical points. There is no solution. Next, we take the second derivative: . If we set this equal to zero, there is also no solution. Therefore, there are no maxima, minima, or points of inflection. Note that the first derivative is always positive. This means that the curve is always increasing. Also notice that the second derivative changes sign from positive to negative at x = –8. This means that the curve is concave up for values of x less than x = –8 and concave down for values of x greater than x = –8.

Now we can draw the curve. It looks like this:

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