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2 2 Equal derivatives Verify that the functions f(x) = sin
Chapter 3, Problem 36AE(choose chapter or problem)
QUESTION:
Verify that the functions \(f(x)=\sin ^{2} x\) and \(g(x)=-\cos ^{2} x\) have the same derivative. What can you say about the difference f - g? Explain.
Questions & Answers
QUESTION:
Verify that the functions \(f(x)=\sin ^{2} x\) and \(g(x)=-\cos ^{2} x\) have the same derivative. What can you say about the difference f - g? Explain.
ANSWER:Solution 36AE Step 1 In this problem we have to verify whether the functions f(x) = sin xand 2 g(x) = cos x have same derivative. 2 2 Given f(x) = sin xand g(x) = cos x f (x) = 2 sin x cos xand g (x) = 2 cos x (sin x) = 2sin x cos x That is f (x) = g(x) Hence f(x)and g(x)have same derivative.