Applying the First Derivative Test In Exercises 17–40, (a) find the critical numbers of f (if any), (b) find the open interval(s) on which the function is increasing or decreasing, (c) apply the First Derivative Test to identify all relative extrema, and (d) use a graphing utility to confirm your results. f ( x ) = { − x 3 + 1 , x ≤ 0 − x 2 + 2 x , x > 0
Applying the First Derivative Test In Exercises 17–40, (a) find the critical numbers of f (if any), (b) find the open interval(s) on which the function is increasing or decreasing, (c) apply the First Derivative Test to identify all relative extrema, and (d) use a graphing utility to confirm your results. f ( x ) = { − x 3 + 1 , x ≤ 0 − x 2 + 2 x , x > 0
Applying the First Derivative Test In Exercises 17–40, (a) find the critical numbers of f (if any), (b) find the open interval(s) on which the function is increasing or decreasing, (c) apply the First Derivative Test to identify all relative extrema, and (d) use a graphing utility to confirm your results.
Find the natural domain and graph the functions in Exercises 15–20.15. ƒ(x) = 5 - 2x 16. ƒ(x) = 1 - 2x - x217. g(x) = sqrt( | x | ) 18. g(x) = sqrt(-x)19. F(t) = t/ | t | 20. G(t) = 1/ | t |
a) Find the domain of f, g, f + g, f – & fg, ff, f/ g
b) Find (f + g)(x), (f – g)(x), (fg)(x), (ff)(x),
For each pair of functions in Exercises 17–32:
15. (8
and g/f.
Find f+ g)(x), (f – g)(x), (fg)(x), (ff)(x),
(f/8)(x), and (g/f)(x).
17. f(x) = 2x + 3, g(x) = 3 – 5x
%3D
18. f(x) = -x + 1, g(x) = 4x – 2
19. f(x) = x – 3, g(x) = Vx + 4
20. f(x) = x + 2, g(x) = Vx – 1
21. f(x) = 2x – 1, g(x) = – 2x²
22. f(x) = x² – 1, g(x) = 2x + 5
23. f(x) = Vx – 3, g(x) :
= Vx + 3
Use graphs to determine if each function f in Exercises 45–48
is continuous at the given point x = c.
[2 – x, if x rational
x², if x irrational,
45. f(x)
c = 2
x² – 3, if x rational
46. f(x) = { 3x +1, if x irrational,
c = 0
[2 – x, if x rational
47. f(x) = { x², if x irrational,
c = 1
x² – 3, if x rational
3x +1, if x irrational,
48. f(x) :
c = 4
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