MONOTONICITY AND MEAN VALUE THEOREM – NAT – LEVEL – 1

If f”(x) > 0 and f’(1) = 0 such that g(x) = f(cot² x + 2cot x + 2) where then g(x) decreasing in (a, b) where is :

Let ‘f’ be a real function whose derivative upto third order exist and for same pair such that a < b. then there exist for which is

If the equation x³ – 3x + k = 0 has two distinct roots in (0,1), then number of values which k can take is :

Let be increasing for all real values of x, then range of a is Find value of

The integral value of ‘b’ for which the function does not passes any stationary point is :

If the function is downward concave is the is

be A and let solution set of equation be B. Now defined a function
If is a strictly decreasing function, then ordered pair satisfying the equation   Find value of

For every pair of continuous function such that max then, for some Find value of

Let
Then the number of critical points on the graph of the function is :

If radians, then the approximate value of cos 60°1′ is given as Find the value of