in the interval π/4 ≤ x ≤ 3π/4, one normal to the graph of f(x)=3cos2x+(sin2)^2 has equation x=k. find the value of k

Question

I do not understand what this question is asking.

Comments

Please check f(x). Is something missing? (sin2)² should perhaps be (sin2x)²? Or (sinx)²?

Answer 1

The only normal which is perpendicular to the x axis is when f(x) has a minimum or maximum (f'(x)=0) between the given limits. So you need to differentiate f and set the derivative to zero. Solve for x. This is the value of k.

Because of the suspected error in the definition of f(x) in the question it isn’t possible to calculate k.