Worksheet for Class 12 Maths Chapter 6 - Applications of Derivatives

Worksheet for Class 12 Maths Chapter 6 – Applications of Derivatives are provided here. The questions are taken as per the syllabus of the CBSE board. Worksheet help the students to secure good marks in the class 12 board examination. The Worksheet provided here covers 1 mark, 2 marks, 4 marks, and 6 marks. 

Class 12 chapter 6 – Application of Derivative covers the important concepts in Maths such as tangents and normals, rate of change, maxima and minima, increasing and decreasing functions, and some simple problems that illustrate the basic concept of derivative and its application in the real-life situations.

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Also, check:

• CBSE Class 12 Mathematics Relations And Functions Worksheet
• Maths MCQs for Class 12 with Answers Chapter 1 Relations and Functions

Class 12 Chapter 6 Applications of Derivatives Worksheet Questions 

Some of the important questions of chapter 6 – Application of Derivative class 12 Maths are provided below as a worksheet format with step by step solutions. Students can score good marks in the final examination by practising these problems, as the below-given problems are important in the examination point of view.

Question 1:

For the given curve: y = 5x – 2x3, when x increases at the rate of 2 units/sec, then how fast is the slope of curve changes when x = 3?

Question 2:

Show that the function f(x) = tan x – 4x is strictly decreasing on [-π/3, π/3]

Question 3:

A stone is dropped into a quiet lake and waves move in the form of circles at a speed of 4 cm/sec. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?

Question 4:

What is the equation of the normal to the curve y = sin x at (0, 0)?

(a)x =0 (b) y=0 (c)x+y =0 (d)x-y=0

Question 5:

Determine all the points of local maxima and local minima of the following function: f(x) = (-¾)x4 – 8x3 – (45/2)x2 + 105

Question 6:

A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at a rate of 0.05 cm per second. Find the rate at which its area is increasing if the radius is 3.2 cm.

Question 7:

Water is dropping out at a constant rate of 1 cubic cm/sec through a small hole at the vertex of the conical container, whose axis is vertical. If the slant height of water in the vessel is 4 cm, find the rate of decrease of slant height, where the vertical angle of the conical vessel is π/6.

Question 8:

Show that the function f(x) = log x/x has maximum at x=e.

Question 9:

Determine the approximate variation in the surface area of a cube of side x metres caused by decreasing the side by 1%.

Question 10:

The radius of a sphere is estimated as 9 cm with an error of 0.03 cm, then calculate the approximate error in measuring its volume.

Question 11:

Calculate two positive numbers whose sum is 15 and the sum of whose squares is minimum.

Question 12:

The length x of a rectangle is decreasing at the rate of 3 cm/ mint and the width y is increasing at the rate of 2cm/min. when x = 10cm and y = 6cm, find the ratio of change of (a) the perimeter (b) the area of the rectangle.

Question 13:

Find the interval in which the function given by f(x) = 4x3 – 6x2 – 72x + 30 is
(a) strictly increasing
(b) strictly decreasing.

Question 14:

Find point on the curveat which the tangents are (i) parallel to x –axis (ii) parallel to y – axis

Question 15:

The volume of a cube is increasing at a rate of 9cm3/s. How fast is the surface area increasing when the length of on edge is 10cm?