List of top Mathematics Questions on Derivatives asked in IPU CET

If the function $f(x) = x^3 - 3x^2 + 6$ is defined on the interval $[0,4]$, the maximum value is
Let \( f(x) = (x^3 + 2)^{30} \). If \( f^{(n)}(x) \) is a polynomial of degree \( 20 \), where \( f^{(n)}(x) \) denotes the \( n + h \)-order derivative of \( f(x) \), then the value of \( n \) is:
A differentiable function \( f(x) \) has a relative minimum at \( x = 0 \), then the function \( y = f(x) + ax + b \) has a relative minimum at \( x = 0 \) for
The function \( f:[0,3] \to [1,29] \) defined by \[ f(x) = 2x^3 - 15x^2 + 36x + 1 \] is
Tangents are drawn from the origin to the curve \(y = \sin x\). Then, the point of contact lie on the curve: