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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...
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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...
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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...
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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 ...
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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 ...
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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...
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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#*...
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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...
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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
………#...
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JEE-Main - Grade 12 - Mathematics - Application of Derivatives - Study ref# 9484
Find the appropriate value of f(2.01), where . Answer: We have
Also,
∴...
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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
...
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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
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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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