The diagram shows the curve $$\(y=\sin 2 x \cos ^{2} x\)$$ for $$\(0 \leqslant x \leqslant \frac{1}{2} \pi\)$$, and its maximum point $$\(M\)$$. Find the exact $$\(x\)$$-coordinate of $$\(M\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_m21_qp_32 Year：2021 Question No：10(b)
Answer:
Use product rule
Obtain correct derivative in any form
Equate derivative to zero and use a double angle formula
Obtain an equation in one trig variable
Obtain \(4 \sin ^{2} x=1,4 \cos ^{2} x=3\) or \(3 \tan ^{2} x=1\)
Obtain answer \(x=\frac{1}{6} \pi\)
Obtain correct derivative in any form
Equate derivative to zero and use a double angle formula
Obtain an equation in one trig variable
Obtain \(4 \sin ^{2} x=1,4 \cos ^{2} x=3\) or \(3 \tan ^{2} x=1\)
Obtain answer \(x=\frac{1}{6} \pi\)
Knowledge points:
3.3.1 understand the relationship of the secant, cosecant and cotangent functions to cosine, sine and tangent, and use properties and graphs of all six trigonometric functions for angles of any magnitude
3.3.2.1 more contents
3.3.2.2 the expansions of
3.3.2.3 the formulae for sin 2A and tan 2A
3.3.2.4 the expression of
3.4.1 use the derivatives of together with constant multiples, sums, differences and composites (Derivatives of are not required.)
3.4.2 differentiate products and quotients
Solution:
Download APP for more features
1. Tons of answers.
2. Smarter Al tools enhance your learning journey.
IOS
Download
Download
Android
Download
Download
Google Play
Download
Download