Multiple Choice Questions

How many extreme values does sin4x 2x where O lt x lt pi 2 have ........

Mathematics (NDA) Diffrentiation

How many extreme values does sin4x + 2x, where O < x < π/2 have ?

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2022 NDA -1 Math

- The function given is $\sin (4 x) + 2 x$ .

- We are looking for extreme values, which include both maxima and minima.

- To find these values, we take the derivative of the function and set it equal to zero:

$\frac{d}{d x} [\sin (4 x) + 2 x] = 4 \cos (4 x) + 2 = 0$

- Solving this equation gives critical points where potential extreme values occur.

- Critical points occur when $\cos (4 x) = - \frac{1}{2}$ .

- The solutions to this in the range $0 < x < \frac{π}{2}$ yield 4 such points due to periodicity and symmetry.

- Correct Answer: Option 3: 4

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