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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

At what points on the curve y = sin x + cos x, 0 ≤ x ≤ 2π, is the tangent line horizontal?

To determine

To find: The points that is the curve have a horizontal tangent.

Explanation

Given:

The function is y=sinx+cosx.

Derivative rules:

(1) Sum Rule: ddx[f(x)+g(x)]=ddx[f(x)]+ddx[g(x)]

(2) Constant Multiple Rule: ddx[cf(x)]=cddx[f(x)]

Calculation:

Obtain the derivative of f(x).

y=ddx(y)=ddx(sinx+cosx)=cosxsinx

Thus, the derivative of  y=sinx+cosx is y=cosxsinx

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