Applications of Derivatives MCQ Quiz in తెలుగు - Objective Question with Answer for Applications of Derivatives - ముఫ్త్ [PDF] డౌన్లోడ్ కరెన్
Last updated on Apr 15, 2025
Latest Applications of Derivatives MCQ Objective Questions
Top Applications of Derivatives MCQ Objective Questions
Applications of Derivatives Question 1:
The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 4x2 + 8x + 5. Find the marginal revenue, when x = 5, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant
Answer (Detailed Solution Below)
Applications of Derivatives Question 1 Detailed Solution
Calculation:
Given: Product R(x) = 4x2 + 8x + 5
The marginal revenue \(\rm {dR(x)\over dx} = {d\over dx}(4x^2 + 8x + 5)\)
⇒ 8x + 8
When x = 5, MR = 8(5) + 8 = 48
Applications of Derivatives Question 2:
A stone is dropped into a quiet lake and waves move in circles at a speed of 5 cm per second. At the instant, when the radius of the circular wave is 15 cm, how fast is the enclosed area increasing?
Answer (Detailed Solution Below)
Applications of Derivatives Question 2 Detailed Solution
Concept;
If y = f(x), then dy/dx denotes the rate of change of y with respect to x.
Decreasing rate is represented by a negative sign whereas the increasing rate is represented by a positive sign.
The area A of a circle with radius r is given by A = πr2
Calculation:
Given: \(\rm \frac {dr}{dt}\) = 5 cm/sec and r = 15
A = πr2
Differentiating with respect to r, we get
⇒ \(\rm \frac{dA}{dt} = π \frac{d(r^2)}{dt}\)
⇒ \(\rm \frac{dA}{dt} = 2πr \frac{dr}{dt}\)
⇒ 2π⋅5⋅15
⇒ 150π