Mathematics Tes...

Let f(x) be a one-to-one function such that f(1) = 3, f(3) = 1, f '(1) = – 4 and f '(3) = 2. If g = f ^–1, then the slope of the tangent line to 1/g at x = 1 is

If g (x³ + 1) = x⁶ + x³ + 2, then the value of g(x² – 1) is

Suppose that f (0) = 0 and f ' (0) = 2, and let g (x) = f (- x + f (f (x))). The value of g ' (0) is equal to

The value of the definite integral,

A line L is perpendicular to the curve  at its point P and passes through (10, –1). The coordinates of the point P are

then the sum of the square of reciprocal of all the values of x where f(x) is non-differentiable, is equal to

h(x) = {x},k(x) = 5^{log₂ (x + 3)} then in [0, 1], Lagranges Mean Value Theorem is NOT applicable to

[Note : where [x] and {x} denote the greatest integer and fractional part function of x respectively]

If the function f (x) = ax e^–bx has a local maximum at the point (2, 10), then

then the value of x satisfying the equation f (x, 10) = f (x, 11), is