12th Class Mathematics Applications of Derivatives Question Bank Case Based (MCQs) - Applications of Derivatives

Directions: (1 - 5)

The Relation between the height of the plant (y in cm) with respect to exposure to sunlight is governed by following equation \[y=4x-\frac{1}{2}{{x}^{2}}\] where x is the number of days exposed to sunlight.

The rate of growth of the plant with respect to sunlight is

A) \[4x-\frac{1}{2}{{x}^{2}}\]

B) \[4\text{ }-\text{ }x\]

C) \[\text{x }-\text{ 4}\]

D) \[x-\frac{1}{2}{{x}^{2}}\]

Correct Answer: B

Solution :

\[y=4x-{{x}^{2}}\] \[\frac{dy}{dx}=4-\frac{1}{2}\times 2x=4-x.\]