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Calculus / Calculus: Early Transcendentals 1 / Chapter 4.6 / Problem 35AE

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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2 2 Equal derivatives Verify that the functions f(x) = tan

Chapter 3, Problem 35AE

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QUESTION:

Verify that the functions \(f(x)=\tan ^{2} x\) and \(g(x)=\sec ^{2} x\) have the same derivative. What can you say about the difference f - g? Explain.

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QUESTION:

Verify that the functions \(f(x)=\tan ^{2} x\) and \(g(x)=\sec ^{2} x\) have the same derivative. What can you say about the difference f - g? Explain.

ANSWER:

Solution 35AE Step 1 In this problem we have to verify whether the functions f(x) = tan xand g(x) = sec x 2 have same derivative. 2 2 Given f(x) = tan xand g(x) = sec x f () = 2 tan x sec xand g(x) = 2sc x (sec x tan x) = 2tan x sec x 2 That is f (x) = g(x) Hence f(x)and g(x)have same derivative.

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