Standard +0.3 This is a straightforward stationary points question requiring differentiation of trigonometric functions, setting the derivative to zero, and solving a basic trigonometric equation (tan 2x = 2/5). While it involves multiple steps and careful handling of the range, it's a standard textbook exercise with no novel insight required, making it slightly easier than average.
A curve has equation \(y = 2\sin 2x - 5\cos 2x + 6\) and is defined for \(0 \leq x \leq \pi\). Find the \(x\)-coordinates of the stationary points of the curve, giving your answers correct to 3 significant figures. [6]
Equate first derivative to zero and arrange to tan2x=...
Obtain tan2x=−0.4
Carry out correct method for finding at least one value of x, dependent *M
Obtain x=1.38
Answer
Marks
Obtain x=2.95 and no others between 0 and π
B1
*M1
A1
DM1
A1
Answer
Marks
A1
[6]
Question 3:
3 | Differentiate to obtain 4cos2x+10sin2x
Equate first derivative to zero and arrange to tan2x=...
Obtain tan2x=−0.4
Carry out correct method for finding at least one value of x, dependent *M
Obtain x=1.38
Obtain x=2.95 and no others between 0 and π | B1
*M1
A1
DM1
A1
A1 | [6]
A curve has equation $y = 2\sin 2x - 5\cos 2x + 6$ and is defined for $0 \leq x \leq \pi$. Find the $x$-coordinates of the stationary points of the curve, giving your answers correct to 3 significant figures. [6]
\hfill \mbox{\textit{CAIE P2 2016 Q3 [6]}}