Advanced Placement Calculus 2016 Graphical Numerical Algebraic Fifth Edition Test Prep Workbook Update
5th Edition
ISBN: 9780328909148
Author: Prentice Hall
Publisher: Prentice Hall
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Sub: BASIC CALCULUS
DETERMINE THE DERIVATIVE OF THE FOLLOWING FUNCTIONS
is a function given as f(x) =
1
We will compute the derivative of f at x = 5 as
Suppose that
2x + 3
follows.
First, we compute and simplify the expression f(5 + h).
f(5 + h) =
Then we compute and simplify the difference quotient, between x = 5 and x = 5 + h.
f(5 + h) – f(5)
h
The derivative of the function at x is the limit of the difference quotient as h approaches zero.
f(5+ h) – f(5)
f'(5):
lim
h
You are given the following function.
10t
G(t) =
t + 7
(a) Find the derivative of the function using the definition of derivative.
G '(t) =
(b) Select the domain of the function.
O (-∞, -7] U [7, 0)
O [-7, 7]
O (-7, 7)
O (∞, -7) U (-7, 0)
(c) Select the domain of its derivative.
O (-0∞, -7] U [7, )
O (7, 7)
O [-7, 7]
O (-0, -7) U (-7, ∞)
OR
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