List of top Mathematics Questions on Applications of Derivatives asked in VITEEE

The function \(f(x)=x^3+ax^2+bx+c\), \(a^2\leq 3b\) has
A spherical balloon is expanding. If the radius is increasing at the rate of 2 centimeters per minute, the rate at which the volume increases (in cubic centimeters per minute) when the radius is 5 centimeters is
The function \( f(x) = x^2 e^{-x} \), \( x>0 \). Then the maximum value of \( f(x) \) is
The angle between the tangents at those points on the curve \( x = t^2 + 1 \) and \( y = t^2 - t - 6 \) where it meets the x-axis is
What is the least value of \( k \) such that the function \( x^2 + kx + 1 \) is strictly increasing on \( (1, 2) \)?