Application of Derivatives2 questions2 PYQ

Application of Derivatives — JEE Maths Practice Questions & Solutions

2 questions on Application of Derivatives with full step-by-step solutions, including past-year (PYQ) problems. Free to practice.

mediumPYQ · JEE Main 2026
Let f:R→Rf:\mathbb{R}\to\mathbb{R} be a differentiable function such that f(x+y3)=f(x)+f(y)3f\left(\dfrac{x+y}{3}\right)=\dfrac{f(x)+f(y)}{3} for all x,y∈Rx,y\in\mathbb{R} and f′(0)=3f'(0)=3. Then the minimum value of g(x)=3+exf(x)g(x)=3+e^x f(x) is
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mediumPYQ · JEE Main 2026
max⁡0≤x≤π(16sin⁡(x2)cos⁡3(x2))\displaystyle\max_{0\le x\le\pi}\left(16\sin\left(\frac{x}{2}\right)\cos^3\left(\frac{x}{2}\right)\right) is equal to
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