   Chapter 11.1, Problem 63E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 59–64, find the equation of the tangent line to the graph of the given function at the point with the indicated x-coordinate. In each case, sketch the curve together with the appropriate tangent line. f ( x ) = x ; x = 4

To determine

To calculate: The slope of tangent to the graph of the function f(x)=x at x=4.Also, sketch the curve and tangent line together.

Explanation

Given Information:

The function is f(x)=x and the point is x=4.

Formula used:

The power rule of derivative, ddx(xn)=nxn1

The equation of a straight line, y=mx+c

Here, m is the slope of the line and c is y intersects.

Calculation:

Consider the function, f(x)=x

Find slope of tangent of graph f(x)=x by determining derivative of the function f(x).

Convert the function f(x)=x to power form,

f(x)=x12

Apply power rule,

f'(x)=12x121=12x12

Convert to positive exponential form,

f'(x)=12x12=12x

So, slope of the function f(x)=x is 12x.

Find slope of function f(x)=x at x=4 by substituting value of x in f'(x)=12x,

f'(4)=124=12(2)=14

Thus, the slope of function f(x)=x at x=4 is 14.

Find the equation of tangent with slope 14 and passing through (4,f(4)).

Put x=1 in the function f(x)=x to find the value of f(4).

f(4)=4=2

Therefore, the tangent is passing through (4,2).

As, equation of line is y=mx+b where m=14 and

b=2(14)4=21=1

So, the equation of tangent is y=14x+1.

Graph:

Consider the equation, f(x)=x

To draw the graph of f(x)=x, first compute values of f(x) at different values of x

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 