In Exercises 5–7 , decide if the function is differentiable at x = 0. Try zooming in on a graphing calculator, or calculating the derivative f ' ( 0 ) from the definition. f ( x ) = { − 2 x for x < 0 x 2 for x ≥ 0
In Exercises 5–7 , decide if the function is differentiable at x = 0. Try zooming in on a graphing calculator, or calculating the derivative f ' ( 0 ) from the definition. f ( x ) = { − 2 x for x < 0 x 2 for x ≥ 0
In Exercises 5–7, decide if the function is differentiable at x = 0. Try zooming in on a graphing calculator, or calculating the derivative
f
'
(
0
)
from the definition.
f
(
x
)
=
{
−
2
x
for
x
<
0
x
2
for
x
≥
0
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
Each of Exercises 25–36 gives a formula for a function y = f(x). In
each case, find f-x) and identify the domain and range of f-. As a
check, show that f(fx)) = f-"f(x)) = x.
25. f(x) = x
26. f(x) = x, x20
%3D
%3D
27. f(x) = x + 1
28. f(x) = (1/2)x – 7/2
30. f(x) = 1/r, x * 0
%3D
29. f(x) = 1/x, x>0
x + 3
31. f(x)
32. f(x) =
VE - 3
34. f(x) = (2x + 1)/5
2
33. f(x) = x - 2r, xs1
(Hint: Complete the square.)
* + b
x - 2'
35. f(x) =
b>-2 and constant
36. f(x) = x?
2bx, b> 0 and constant, xsb
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