   Chapter 2.R, Problem 53E

Chapter
Section
Textbook Problem

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

To determine

To find:

x at which curve y=sinx+cosx   0xπ/2 is horizontal.

Explanation

1) Formula:

i. Sum rule:

ddxfx+gx=ddxfx+ddxg(x)

ii. ddxsinx=cosx

iii. ddxcosx=-sinx

iv. Equation of tangent line to the curve y=f(x) at point (a,f(a)) is, (y-f(a))=f(a)(x-a)

2) Given:

y=sinx+cosx   0xπ/2

3) Calculation:

Differentiate given equation of curve with respect to x,

f'x=ddx[sinx+cosx]

Using sum rule,

ddxsinx+cosx=ddxsinx+ddxcosx=cosx-sinx

Tangent line on curve is horizontal if f'x=0

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