Applications of Derivatives
Higher Order Derivatives
nta_pyq_2024_apr
Grade 12
Question:
If $y(\theta)=\dfrac{2\cos\theta+\cos2\theta}{\cos3\theta+4\cos2\theta+5\cos\theta+2}$, then at $\theta=\dfrac{\pi}{2}$, $y''+y'+y$ is equal to:
$\dfrac{1}{2}$
1
2
$\dfrac{3}{2}$
Step-by-Step Solution
Key Concept: Simplify $y$: factor numerator and denominator. $y=\dfrac{1}{2}\cdot\dfrac{1}{1+\cos\theta}$. Differentiate twice and evaluate at $\theta=\pi/2$.
$y=\frac{1}{2(1+\cos\theta)}$. At $\theta=\pi/2$: $y=1/2$, $y'=1/2$, $y''=1$. $y''+y'+y=2$.
Correct Answer: 3