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CBSE - Class 12 > Mathematics > Application of Derivatives Worksheets

Free CBSE - Class 12 Mathematics - Application of Derivatives worksheets

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Here is a Sample Worksheet for you to Practice. Download this worksheet to see the answers.

1.
For all real values of $x$, the minimum value of $\frac{1-x+x^2}{1+x+x^2}$ is
1. 0 2. 1 3. 3 4. $\frac{1}{3}$
2.
The maximum value of $[x(x-1)+1]^{\frac{1}{3}}$, $0 \le x \le 1$ is
1. $(\frac{1}{3})^{\frac{1}{3}}$ 2. $\frac{1}{2}$ 3. 1 4. 0
3.
Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base.
4.
Of all the closed cylindrical cans (right circular), of a given volume of $100$ cubic centimetres, find the dimensions of the can which has the minimum surface area?
5.
A wire of length $28$ m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?
6.
Prove that the volume of the largest cone that can be inscribed in a sphere of radius $R$ is $\frac{8}{27}$ of the volume of the sphere.
7.
Show that the right circular cone of least curved surface and given volume has an altitude equal to $\sqrt{2}$ time the radius of the base.
8.
Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is $\tan^{-1} \sqrt{2}$.
9.
Show that semi-vertical angle of right circular cone of given surface area and maximum volume is $\sin^{-1}(\frac{1}{3})$.
10.
The point on the curve $x^2 = 2y$ which is nearest to the point $(0, 5)$ is
1. $(2\sqrt{2},4)$ 2. $(2\sqrt{2},0)$ 3. $(0, 0)$ 4. $(2, 2)$
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Chapters in CBSE - Class 12 Mathematics

Application of Integrals Worksheet Continuity and Differentiability Worksheet Determinants Worksheet Differential Equations Worksheet Integrals Worksheet Inverse Trigonometric Functions Worksheet Linear Programming Worksheet Matrices Worksheet Probability Worksheet Relations and Functions Worksheet Three Dimensional Geometry Worksheet Vector Algebra Worksheet

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Top Concept Videos in Mathematics Application of Derivatives

The Turning Points and Slopes of Curves video thumbnail

The Turning Points and Slopes of Curves

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