r''ii

I

26.

25. Graph. Dashed line is the derivative.(Equation is f(x) = xsl24 - x2l8 - x + 2.)

Graph. Dashed line is the derivative.(Equation is g(x) = -x3/9 + 22/3 + x - l.l

27. Numerical versus Exact Derivative Problema. Graph. f(x) = 9.4x3 -7x + 4

b. The graph of f is shown dotted in part (a).c. There appear to be only two graphs because the

exact and the numerical derivative graphs almostcoincide.

d. f(3) = -6.2f'(3) = 3.8 (by formula)f(3) = 3.8000004 (depending on grapher)The two values of f'(3) are almost identical!

28. Power Formula for Various Types of Exponentsa. g(x) = 11 : Conjecture: g'(x) = -1 'r 2. Graph.

Conjecture is confirmed.

b. h(x) = x1l2: Conjecture: g'(x) = Q.g;-1l2. Graph.Conjecture is confirmed.

v',2

I

It

Yt

e(x) = !x; Conjecture: e'(x) = x'2x-t. Graph.Conjecture is refuted!

29.f(x) =7.1t2*2x-13t'i 1x1 = f,r-t rz + 2, 1' (41 =f;lncreasing by 9/4 y-units per x-unit at x = 4

30.f(x) =r(-2-3x+11f'(x) = -lx-3 - 3, f'(1) = -5Decreasing by 5 y-units per x-unit ?t x = 1

31. f(x) - x1'5 - 6x + 30f'(x) = 1.S;o.s - 6, f'(9) = -1.5Decreasi4g by 1.5 y-units per x-unit at x = I

32.f(x)=-3{x+x+1t'(xl = -lltn + 1, f'(2) = -0.0607Decreasing by 0.0607 y-unit per x-unit at x = 2

-333. f(x) =?- *t -3x + 5, f'(x) = x2 -2x-3,Graph.

High and low points of the f graph are at the x-intercepts of the f' graph.

-33a. l(x) =i - Zxz+ 3x + 9, f'(x) = x2 - 4x + 3. Graph.

High and low points of the f graph are at the x-interceptsol the f'graph.

x

I

3

32 Cqlculus: Concepts ond Applicotions Problem Ser 3-4