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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

For what value of x does the graph of f(x) = ex2x have a horizontal tangent?

To determine

To find: The value of x on the function that has a horizontal tangent.

Explanation

Given:

The function f(x)=ex2x.

Derivative rules:

(1) Constant Multiple Rule: ddx[cf(x)]=cddxf(x)

(2) Power Rule: ddx(xn)=nxn1

(3) Difference Rule: ddx[f(x)g(x)]=ddx(f(x))ddx(g(x))

(4) Exponential function: ddx(ex)=ex

Calculation:

The derivative of f(x) is computed as follows,

f(x)=ddx(f(x)) =ddx(ex2x) 

Apply the difference rule (3) and the constant multiple rule (1),

f(x)=ddx(ex)ddx(2x)  =ddx(ex)2ddx(x)  

Apply the power rule (2)

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