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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding an Equation of a Tangent Line In Exercises 41-44, find an equation of the tangent line to the graph of the function at the given point.

y = x 3 e x ,       ( 3 , 27 e 3 )

To determine

To calculate: The equation of the tangent line to the graph of the function y=x3ex at the point (3,27e3).

Explanation

Given Information:

The provided function is y=x3ex.

Formula used:

If the function is f(x)=eax, then the chain rule for the derivative of the function is given by.

f(x)=eududx

Where u=ax

If f(x) and g(x) are two functions then product of derivative of functions is,

ddx[f(x)g(x)]=g(x)f(x)+f(x)g(x)

The equation of the line is given by point-slope formula, yy1=m(xx1)

Where m is the slope of the equation and (x1,y1) is the coordinate on the graph of the line.

Calculation:

Consider the function, y=x3ex

Evaluate the derivative of the function by applying product rule.

y=ddxx3ex=exddxx3+x3ddxex=3x2ex+x3e

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