   Chapter 11, Problem 13RE ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Write the equation of the line tangent to y = 4 e x 3 at  x = 1.

To determine

To calculate: The equation of the line tangent to the curve y=4ex3 at x=1.

Explanation

Given Information:

The provided equation of the curve is:

y=4ex3

The provided point is x=1.

Formula used:

The slope of tangent to a curve y=f(x) at point (x,y) is given by the derivative of the curve at that point.

The equation of a line passing through points (x1,y1) and slope m is given by:

yy1=m(xx1)

Calculation:

Consider the provided equation of curve:

y=4ex3

Now, find the derivative dydx from y=4ex3 by taking the derivative term by term on both sides of the equation as:

ddx(y)=ddx(4ex3)dydx=4ex33x2y=12x2ex3

Now, the provided point is x=1

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