What is the slope of the tangent of y = cos ^-1 (cos x) at x = \(-\frac{\pi}{5}\) ?

The maximum value of \(\sin \left( {{\rm{x}} + \frac{{\rm{\pi }}}{6}} \right) + \cos \left( {{\rm{x}} + \frac{{\rm{\pi }}}{6}} \right)\) in the interval \(\left( {0,\frac{{\rm{\pi }}}{2}} \right)\)  is attained at

What is the minimum value of [x(x – 1) + 1] ^1/3 , where 0 ≤ x ≤ 1?

What is the least value of m(θ) ?

Let P be the median, Q be the mean and R be the mode of observations x_1, x_2, x₃, .....x_n. Let \(S=\sum_{i=1}^n\left(2 x_i-a\right)^2\) S takes minimum value, when a is equal to

What is the maximum value of xy ?

Consider the following statements in respect of the function f(x) = sin x:

1. f(x) increases in the interval (0, π).

2. f(x) decreases in the interval  \(\left(\dfrac{5\pi}{2},3\pi\right).\)

Which of the above statements is/are correct?

What is the maximum value of sin 2x ⋅ cos 2x?

How many extreme values does sin4x + 2x, where \(0 < x < \frac{\pi}{2} \) have ?

What is the slope of the tangent of y = cos ^-1 (cos x) at x = \(-\frac{\pi}{5}\) ?

The maximum value of \(\sin \left( {{\rm{x}} + \frac{{\rm{\pi }}}{6}} \right) + \cos \left( {{\rm{x}} + \frac{{\rm{\pi }}}{6}} \right)\) in the interval \(\left( {0,\frac{{\rm{\pi }}}{2}} \right)\)  is attained at

The derivative of the function y = 3|x| + 1 at the point x = 0 is

Given that f(x) = x ^1/x , x > 0 has the maximum value at x = e, then