JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Introduction and Snapshot of Application of Derivatives - Study ref# 914

Introduction
In this chapter, we will study
applications of the derivative in various disciplines, e.g., in engineering,
science, social science, and many other fields. For instance, we will learn
how the derivative can be used (i) to det... read more

JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Introduction and Snapshot of Application of Derivatives - Study ref# 915

Following sections must be covered to
understand the Application of Derivative:
1. Rate of Change of Quantities
2. Increasing and Decreasing Functions
3. Tangents and Normals
4. Approximations
5. Maxima and Minima... read more

JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Target Setup for Application of Derivatives - Study ref# 916

Student requires to achieve the following milestones to get better grip over Application of Derivative. The milestones / targets are as follows: Starting Point: Days 0Test TypeAppear on TestTarget TestsScorePractice Test000%Chapt... read more

JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Study ref# 9465

The volume of a cube in increasing at the
rate of . How fast is
the surface area increasing when the length of an edge is Answer: Let at any instant of time the edge of
the cube be surface
area be S and the volume be V, then
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JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Study ref# 9466

A stone is dropped into a quite lake and
waves move in circles at the speed of 5 cm/s. At the instant when the radius
of the circular wave is 8cm, how fast is the enclosed area increasing ? Answer: Let at any instant of time the radius
of ... read more

JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Study ref# 9467

The radius of a circle is increasing at
the rate of 0.7 cm/s. What is the rate of increase of its circumference ? Answer: Let at any instant of time the radius
of the circular be r and its circumference be C, then
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JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Study ref# 9468

A ladder 5cm long is leaning against a
wall. The bottom of the ladder is pulled along the ground , away from the
wall, at the rate of 2cm/s. How fast is its height on the wall decreasing
when the foot of the ladder is 4m away from the ... read more

JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Study ref# 9469

The radius of an air bubble is increasing
at rate of At
what rate is the volume of the bubble increasing when the radius is 1cm? Answer: Let at any instant of time the radius
of the bubble be r and its volume be V, then
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JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Study ref# 9470

The total revenue in rupees received from
the sale of x units of a product is given by . Find the
marginal revenue when x=7. Answer: We have . Answer: We have ………..(i)
Differentiat... read more

JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Study ref# 9481

For the curve , find all
the points at which the tangent passes through the origin. Answer: Let be the
required point on the given curve#*... read more

JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Study ref# 9482

Prove that the curves and cut at right
angles if Answer: We have ………..(i)
and ……….(ii)
Solving (i) &a... read more

JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Study ref# 9483

Find the equation of the tangent to the
curve which is
parallel to the line . Answer: We have ……..(i)
and ………#... read more

JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Study ref# 9484

Find the appropriate value of f(2.01),
where . Answer: We have
Also,
∴... read more

JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Study ref# 9485

Find the approximate change in the volume
V of a cube of side x meters caused by increasing the side by 1%. Answer: We have
and
... read more

JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Study ref# 9486

The approximate change in the volume of a
cube of side x meters caused by increasing the side by 3% is
(A) 0.06 (B)
0.6
(C) 0.09 read more

JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Study ref# 9487

Prove that the following functions do
not have maxima or minima:
Answer: We have ,
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JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Study ref# 9488

Prove that the following functions do
not have maxima or minima:
Answer: We have , .
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JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Study ref# 9489

Find the maximum and minimum values of on Answer: Let
For critical points ,let
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