# Calculus for Parallel Lines of Graphs

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If f(x) =7x + 11 and g(x) =5x- 1, find f(g(x)). What is f(g(2))?

Find the average rate of change of the function shown below over the given interval. y=-3x^2 - x, [5, 6]

Find the limit, if it exists. 〖lim┬(x→4) (x^2+4x-32)/(x^2-16) 〗〖〖^〗〗

Find an equation for the tangent to the curve at the given point. y=x^2- x, (-4,20)

Calculate the derivative of the function. Then find the value of the derivative as specified. f(x)= x^2+ 7x- 2; f (0)

Solve. Find the point where the graph of the function has a horizontal tangent. f(x)=4x^2+ 5x+ 2

Find all points "x" where the function whose graph is shown below is discontinuous.

A function f(x), a point c, the limit of f(x) as x approaches c, and a positive number ɛ is given. Find a number δ> 0 such that for all x,0<|x - c|<δ ⟶ |f(x)- L| <ɛ.

f(x)=5x+ 9, L=29, c=4, and ɛ= 0.01

Use the graph of the function f(x) to evaluate the limit, or state that the limit does not exist.

〖lim┬(x→0) f(x)〗〖〖^〗〗

Find an equation of the line passing through the given point and parallel to the graph of the function shown. Write the equation using function notation. 10) Through (7,3); parallel to f(x)=4x- 6

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#### Solution Preview

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1. If f(x) =7x + 11 and g(x) =5x- 1, find f(g(x)). What is f(g(2))?

Solution:

f(g(x)) = f(5x-1) = 7(5x-1)+11 = 35x-7+11 = 35x + 4

Put x = 2 in f(g(x)) = 35x + 4 to find the value of f(g(2))

f(g(2)) = 35(2)+4 = 70+4 = 74

2. Find the average rate of change of the function shown below over the given interval. y=- - x, [5, 6]

Solution:

Average rate of change =

Answer: -34

3. Find the limit, if it exists.

Solution:

Answer: 3/2

4. Find an equation for the tangent to the curve at the given point. y= - x, (-4,20)

Solution:

Slope = (-4) = 2(-4)-1 = -9

Equation of tangent ...

#### Solution Summary

This posting includes detailed solutions to some questions on finding derivatives, slope of a tangent line and equation of a parallel line through a given point.