List of top Mathematics Questions on Differential Calculus asked in JEE Main

If $ y = f(x) $ satisfies the differential equation \[ (x^2 - 4)y' - 2xy + 2x(4 - x^2)^2 = 0 \] and $ f(3) = 15 $, then find the local maximum value of $ f(x) $:

If the function $ f(x) = 2x^3 - 9ax^2 + 12a^2x + 1 $, where $ a>0 $, attains its local maximum and minimum at $ p $ and $ q $, respectively, such that $ p^2 = q $, then $ f(3) $ is equal to:

Let $ f : \mathbb{R} \to \mathbb{R} $ be a twice differentiable function such that \[ (\sin x \cos y)(f(2x + 2y) - f(2x - 2y)) = (\cos x \sin y)(f(2x + 2y) + f(2x - 2y)), \] for all $ x, y \in \mathbb{R}. $

If $ f'(0) = \frac{1}{2} $, then the value of $ 24f''\left( \frac{5\pi}{3} \right) $ is:

If $y(\theta) = \frac{2\cos\theta + \cos2\theta}{\cos3\theta + 4\cos2\theta + 5\cos\theta + 2}$, then at $\theta = \frac{\pi}{2}, y'' + y' + y$ is equal to: