JEE Main 2025 — Application of Derivatives Questions with Solutions

Let x=-1 and x=2 be the critical points of the function f(x)=x³+ax²+b c|x|+1, x ≠ 0. Let m and M respectively be the ab…

Let f: R → R be a function defined by f(x)=\|x+2|-2| x\|. If m is the number of points of local minima and n is the num…

The shortest distance between the curves y²=8 x and x²+y²+12 y+35=0 is :

If the set of all values of a, for which the equation 5 x³-15 x-a=0 has three distinct real roots, is the interval (α,…

Let a 0. If the function f(x)=6 x³-45 a x²+108 a² x+1 attains its local maximum and minimum values at the points x₁ and…

Let (2,3) be the largest open interval in which the function f(x)=2 e(x-2)-x²+a x+1 is strictly increasing and (b, c) b…

Let f: R → R be a polynomial function of degree four having extreme values at x=4 and x=5. If x → ₀ (f(x))/(x²)=5, then…

Let f be a differentiable function on R such that f(2) = 1, fⁱme(2)=4. Let x → ₀(f(2+x))³ / x=e^α. Then the number of t…

If the function f(x)=2 x³-9 ax²+12 a² x+1, where a 0, attains its local maximum and local minimum values at p and q, re…

The sum of all local minimum values of the function f(x)= \arraylr 1-2 x, & x -1 \ (1)/(3)(7+2|x|), & -1 ≤ x ≤ 2 \ (11)…