JEE Main Mathematics — Application of Derivatives Previous-Year Questions

Let f be a differentiable function satisfying f(x)=1-2 x+∫₀x e⁽x⁻t⁾ f(t) dt, x R and let g(x)=∫₀x(f(t)+2)¹⁵(t-4)⁶(t+12)…

Let f(x)=x²⁰²⁵-x²⁰⁰⁰, x [0,1] and the minimum value of the function f(x) in the interval [0,1] be (80)⁸⁰(n)⁻⁸¹. Then n…

Let f: R → R be a differentiable function such that f ((x+y)/(3) ) = (f(x) + f(y))/(3) for all x, y R, and f'(0) = 3. T…

Let f: R → R be a twice differentiable function such that the quadratic equation f(x) m²-2 fⁱme(x) m+fⁱme ⁱme(x)=0 in m…

Consider the following three statements for the function f:(0, ∞) → R defined by f(x)= | e x |-|x-1| : (I) f is differe…

Let (2 α, α) be the largest interval in which the function f(t)=|t+1|t², t 2, is \\\\_

Let f(x) be a polynomial of degree 5, and have extrema at x = 1 and x = -1. If → ₀ ((f(x))/(x³) ) = -5, then f(2) - f(-…

The number of critical points of the function f(x) = cases |( x)/(x) |, & x ≠ 0 \ 1, & x = 0 cases in the interval (-2π…

₀ ≤ x ≤ π (16 ((x)/(2) )³ ((x)/(2) ) ) is equal to:

Let f: R → R be a twice differentiable function such that f''(x) > 0 for all x R and f'(a-1) = 0, where a is a real num…