List of top Mathematics Questions on Applications of Derivatives asked in MHT CET

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

If \( f(x) = 3x^3 + 2x^2 f'(1) + x f''(2) + f'''(3) \) then \( f(x) = ....... \)}

The combined equation of the tangent and normal to the curve \( xy = 15 \) at the point (5, 3) is

The minimum value of the slope of the tangent to curve $y = x^3 - 3x^2 + 2x + 93$ is

20 is divided into two parts so that the product of the cube of one part and the square of the other part is maximum, then these two parts are

If \(x\) is real, then the difference between the greatest and least values of \(\frac{x^2 - x + 1}{x^2 + x + 1}\) is

The minimum value of the slope of the tangent to curve $y = x^3 - 3x^2 + 2x + 93$ is

Three urns respectively contain 2 white and 3 black, 3 white and 2 black and 1 white and 4 black balls. If one ball is drawn from each um, then the probability that the selection contains 1 black and 2 white balls is

An open tank with a square bottom is to contain 4000 cubic cm . of liquid. The dimensions of the tank so that the surface area of the tank is minimum, is

The minimum value of the slope of the tangent to curve $y = x^3 - 3x^2 + 2x + 93$ is