Barrons AP Calculus - David Bock

substitute this in the equation of the curve, we get

Thus y = ±1 and x = ±2. The points, then, are (2, −1) and (−2, 1).

EXAMPLE 8

Find the x-coordinate of any point on the curve of y = sin^2 (x + 1) for which the tangent is

parallel to the line 3x − 3y − 5 = 0.

SOLUTION: Since = 2sin(x + 1) cos(x + 1) = sin2(x + 1) and since the given line has slope

1, we seek x such that sin 2(x + 1) = 1. Then

or

BC ONLY

EXAMPLE 9

Find the equation of the tangent to F(t) = (cos t, 2 sin^2 t) at the point where

SOLUTION: Since we see that

C. INCREASING AND DECREASING FUNCTIONS

CASE I. FUNCTIONS WITH CONTINUOUS DERIVATIVES.

A function y = f (x) is said to be on an interval if for all a and b in the interval such that a <

b, To find intervals over which f (x) that is, over which the curve analyze the

signs of the derivative to determine where

EXAMPLE 10

For what values of x is f (x) = x^4 − 4x^3 , increasing? decreasing?

SOLUTION: f ′(x) = 4x^3 − 12x^2 = 4x^2 (x − 3).