For each function in Exercises 1-16 , (a) find the simplified from of the different of the different quotient and then (b) complete the following table, x h f ( x + h ) − f ( x ) h 5 2 5 1 5 0.1 5 0.01 f ( x ) = x 2 − 3 x a. (a) 2 x + h − 3 b. (b) 9 , 8 , 7.1 , 7.01
For each function in Exercises 1-16 , (a) find the simplified from of the different of the different quotient and then (b) complete the following table, x h f ( x + h ) − f ( x ) h 5 2 5 1 5 0.1 5 0.01 f ( x ) = x 2 − 3 x a. (a) 2 x + h − 3 b. (b) 9 , 8 , 7.1 , 7.01
Solution Summary: The author explains the simplified form of the difference quotient of f(x)=x
For each function in Exercises 1-16, (a) find the simplified from of the different of the different quotient and then (b) complete the following table,
Evaluate the difference quotient for the following function.
f(x) = 4x² - x
First, find
f(x + h) - f(x)
h
4 (z + h) ² − (z + h) − ( 4z² − z)
4(a+h)²-(x+h)-(4x²-x)
h
Next, simplify the numerator.
(8x+4h-1)
Divide out the h.
8x +4h-1
So now, find the limit
lim
A-0
f(x+h)-f(x)
h
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Use the function f(x) = -3x? + 7x + 7 to compute and expand and simplify the following.
a. f(-2) =
b. f(x) +h =
c. f(x + h) =
d. f(x + h) – f(x) =
Which of the following functions has an inverse?
xlxl
, (d) 4x5 + x² - 15, (e) **
x2 +1
x+1
(a) x³ + x - 1, (b) x³ - x + 1, (C)-
x-1
O A. only (a)
B. only (C) and (e)
C. only (a) and (b)
O D. only (a), (c), and (e)
E. none of the above
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