Derivatives of Functions: JEE Questions & Solutions

Let f(x) = x^3 + x^2 f'(1) + 2x f''(2) + f'''(3), x R. Then the value of f'(5) is:

Let f: R R be a twice differentiable function such that f''(x) ( x2) + f'(2x - 2y) = ( x) (y + 2x) + f(2x - 2y) for all x, y R. If f(0) =…

Let f be a differentiable function on R such that f(2) = 4. Let x 0 ( f(2+x))^3/x = e^. Then the number of times the curve y = 4x^3 - 4x^2…

Given f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3), x R. Then f'(10) is equal to:

Let g(x) = 3f ( x3) + f(3 - x) where f''(x) 0 for all x (0,3). If g is decreasing in (0,) and increasing in (,3), what is 8 ?

Suppose f(x) = (2x + 2^-x) (x) ^-1(x^2 - x + 1). The value of f'(0) is equal to:

Let f(x) = 2x - x^2, x R. If m and n are respectively the number of points at which the curves y = f(x) and y = f'(x) intersect the x-axis,…

Let y = ( 1 - x^21 + x^2), -1 < x < 1. Then at x = 12, the value of 225(y' - y'') is equal to:

Let f(x) = 2x - x^2, x R. If m and n are respectively the number of points at which the curves y = f(x) and y = f'(x) intersect the x-axis,…

If e y = 3 ^-1 x, then (1 - x^2) y'' - x y' at x = 12 is equal to:

If f(x) = x^3 - x^2 f'(1) + x f''(2) - f'''(3), x R, then:

If 2^xy + 3^y^x = 20, then dydx at (2,2) is equal to: