FIGURE N3–6
From the graphs above we can make the following observations:
(1) At the points where the slope of f (in Figure N3–5) equals 0, the graph of f ′(Figure N3–6) has
x-intercepts: approximately x = −1.8 and x = 1.1. We’ve drawn horizontal broken lines at these points
on the curve in Figure N3–5.
(2) On intervals where f the derivative is We see here that f decreases for x <
−1.8 (approximately) and for x > 1.1 (approximately), and that f increases for −1.8 < x < 1.1
(approximately). In Chapter 4 we discuss other behaviors of f that are reflected in the graph of f ′.
BC ONLYF. DERIVATIVES OF PARAMETRICALLY DEFINED
FUNCTIONS
Parametric equations were defined previously in Chapter 1.
If x = f (t) and y = g(t) are differentiable functions of t, then
EXAMPLE 24
If x = 2 sin θ and y = cos 2θ, findSOLUTION:Also,