# The given curve have no tangent line with the slope 4 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 3.1, Problem 51E
To determine

## To show:The given curve have no tangent line with the slope 4

Expert Solution

x cannot be negative number.

### Explanation of Solution

Given:

The curve is

y=6x3+5x3

Slope =4

Concept used:

The equation is in slope −intercept form, y=mx+c

An equation for the line through the point (x1,y1) with slope m is

yy1=m(xx1)

Calculation:

The function

y=6x3+5x3.......................(1)

The derivative of a function

y=f(x)y=f(x)=dydx=m

Differentiating the equation (1) with respect to x

y=6x3+5x3y=18x2+5........................(2)

In order to have a tangent line with slope 4

18x2+5=4x2=118

For real numbers x cannot negative number

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