Q231 / 270 · NDA 2020 · Mathematics

What is the minimum value of $3 \cos \left(A+\frac{\pi}{3}\right)$ where $A \in R$ ?

  • Correct answer
    A
    -3
  • B
    -1
  • C
    0
  • D
    3

Solution

Let $y=3 \cdot \cos \left(A+\frac{\pi}{3}\right), y^{\prime}=-3 \cdot \sin \left(A+\frac{\pi}{3}\right)$ For extremum value, $y^{\prime}=0$ $\begin{aligned} & \sin \left(A+\frac{\pi}{3}\right)=0 \Rightarrow A+\frac{\pi}{3}=0 \Rightarrow A=-\frac{\pi}{3} \\ & y^{\prime \prime}=-3 \cdot \cos \left(A+\frac{\pi}{3}\right) \\ & \quad=-3 \cos \left(-\frac{\pi}{3}+\frac{\pi}{3}\right)=-3 \cos (0)=-3 \end{aligned}$

Hence, the correct answer is option: 'A'.

Relevant Questions