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 + 4 x − 3 a. 2 x + h + 4 ; b. 16 , 15 , 14.1 , 14.01
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 + 4 x − 3 a. 2 x + h + 4 ; b. 16 , 15 , 14.1 , 14.01
Solution Summary: The author explains the simplified form of the difference quotient of f(x) = 2+4x-3.
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,
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) =
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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Which set of words describes the end behavior of the function f(x)=0.4(2x−9)(3x+1)(x−7)(x+9)?
a) increasing to the left and to the right
b) decreasing to the left and to the right
c) increasing to the left and decreasing to the right
d) decreasing to the left and increasing to the right
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