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Chapter 2: Q. 63 (page 185)

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The line that passes through the point (3,2)and is parallel to the tangent line to f(x)=1x at x=-1.

Short Answer

Expert verified

The equation isy=-x+5

Step by step solution

01

Step 1.Given information

Given the functionf(x)=1xand the pointx=-1

02

Calculate the tangent line

Calculating, we get

y=-1+(-1x2)(x+1)y=-1-x-1x2

03

Calculate the line

Calculating, we get

y-2=-1(x-3)y-2=-x+3y=-x+5

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Most popular questions from this chapter

Differentiation review: Without using the chain rule find the derivative of each of the function f that follows some algebra may be required before differentiating

a)f(x)=(3x+1)4b)f(x)=(1x+1x2)2c)f(x)=(x+1)2xd)f(x)=(x+1)2x

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=1x2+1

Each graph in Exercises 31鈥�34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=3x2+18-7x-23

Velocity v(t) is the derivative of position s(t). It is also true that acceleration a(t) (the rate of change of velocity) is the derivative of velocity. If a race car鈥檚 position in miles t hours after the start of a race is given by the function s(t), what are the units of s(1.2)? What are the units and real-world interpretation of v(1.2)? What are the units and real-world interpretations of a(1.2)?
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