List of top Mathematics Questions on Applications of Derivatives asked in CUET (UG)

Find the equation of the tangent to \[ y=x^3-3x+1 \] at the point where \(x=2\).

Find the rate of change of the area of a circle with respect to its radius \(r\) when \[ r=3\text{ cm}. \]

Find the slope of the normal to the curve \( y = 2x^2 + 3\sin x \) at the coordinate point where \( x = 0 \).

Find the interval in which the function \( f(x) = 2x^3 - 3x^2 - 36x + 7 \) is strictly increasing:

Find the equation of the normal to the curve \( y = x^2 - x \) at the coordinate point position \( (1, 0) \).

Find the open interval across which the cubic polynomial function \( f(x) = 2x^3 - 3x^2 - 36x + 7 \) is classified as strictly decreasing.