Page 78 - Calculus Workbook For Dummies

62 Part III: Differentiation

Q. What’s the slope of the parabola 3. Factor out h.
2
f x = 10 - x at x = 3? h - 2 x - hh
^
^ h
= lim
h " 0 h
A. The slope is –6.
4. Cancel.
2
1. Because f x = 10 - x , then
^ h
2 = lim - 2 x - hh
^
h =
f x + h 10 - ^ x + hh , and so the h " 0
^
derivative is
5. Plug in the arrow-number.
2 2
10 - ^ x + h 10 - x i
h - _
x =
f l ^ h lim = - 2 x - 0
h " 0 h
x = -
f l ^ h 2 x
2. Simplify.
6. You want the slope or derivative at
2
2
10 - _ x + 2 xh + h i - 10 + x 2 x = 3, so plug in 3.
= lim
h " 0 h f l ^ h 2 3
3 = - $
2
2
10 - x - 2 xh - h - 10 + x 2
= lim = - 6
h " 0 h
- 2 xh - h 2
= lim
h " 0 h
7. Use the difference quotient to determine 8. Use the difference quotient to find the
2
the derivative of the line y = 4 x - 3. derivative of the parabola f x = 3 x .
^ h
Solve It Solve It