Question

嗨 你好 我需要幫忙

求解21,22,38🙇 section1.3不用理他 equation 2.1.5是微分的定義式

(d) Use the definition of derivative to prove that your guess
in part (c) is correct.
14-21 Find the derivative of the function using the definition of
derivative. State the domain of the function and the domain of its
derivative.
14. f(x) = 3x - 8
15) f(x) = mx + b
16. f(x) - 4 + 8x - 5x?
(17) f(x) = x - 3x + 5
18. f(x) - x + V
g(x) - 19-
x? - 1
20. f(x)
21s(x) x2
2.x - 3
(hours)
arger. The graph
hat the battery
purs).
(r)?
graph
-
a
22.) a) Sketch the graph of f(x) - V6 - x by starting with
the graph of y
# and using the transformations of
Section 1.3.
(b) Use the graph from part (a) to sketch the graph of f!
(c) Use the definition of a derivative to find f'(x). What are
the domains of f and f'?
(d) Use a graphing device to graph f' and compare with your
sketch in part (b).
lo-TE
23. (a) If f(x) = x + 1/x, find f'(x).
(b) Check to see that your answer to part (a) is reasonable by
JE
comparing the graphs of f and f'.
1 (hours)
shows how
24. The table given tho hai

Z
(b) Use the acceleration curve from par (a) to estimate the
10 seconds. What are the units for jerk?
45) The lel
defined
|||||
V has a vertical tangent line at (0,0).
and
jerk at =
38, Let f(x) = V.
x
(
(a) If a 40. use Equation 2.1.5 to find s'a).
(b) Show that f'(o) does not exist.
(c) Show that y-
(Recall the shape of the graph of f. See Figure 1.2.13.)
39. (a) If g(x) = x?, show that g'(0) does not exist.
(b) Ifa * 0, find g'(a).
(c) Show that y = x2 has a vertical tangent line at (0,0).
c
(d) Illustrate part (c) by graphing y - x2)
if the
sided
(a) F
|
40. Show that the function f(x) = |x - 6 is not differentiable
at 6. Find a formula for and sketch its graph.
(b)
Where is the greatest integer function () = [x] not