The volume of a cube is increasing at the rate of 9 cubic centimetres per second. How fast is the surface area increasing when the length of an edge is 10 centimetres?

3

(a)

Show that the function  given by:
\(f(x)=7x-3\) is strictly increasing on R.

3

(a)

The total cost C(x) in Rupees associated with the production of x units of an item is given by
\(C(x)=0.007x^{ 3 }-0.003x^{ 2 }+15x+4000\)
Find the marginal cost when 17 units are produced.

3

(a)

The total revenue in Rupees received from the sale of x units of a product is given by
\(R(x)=13x^{ 2 }+26x+15\)
Find the marginal revenue when x = 7

3

(a)

Prove that the function given by 
\(f(x)=x^{ 3 }-3x^{ 2 }+3x-100\quad \)

3

(a)

Prove that the function f(x) = tan x - 4x is strictly decreasing on \(\left( -\frac { \pi }{ 3 } ,\frac { \pi }{ 3 } \right) \)

3

(a)

Find all the points of local maxima and local minima of function \('f'\) is given by\(f(x)=2x^{ 3 }-6x^{ 2 }+6x+5\)

3

(a)

Find the absolute maximum and minimum values of the function 'f' is given by:
\(f(x)=cos^{ 2 }x+sinx,x\in [0,\pi ]\)

3

(a)

Show that the function\(f(x)=4x^{ 3 }-18x^{ 2 }+27x-7\)  has neither maximum nor minimum.

3

(a)

Find the equations of the tangent  and normal to the curve x = 1-\(cos\theta ,y-=\theta -sin\theta \) at \(\theta =\frac { \pi }{ 4 } \)

3

(a)

Find the equations of the tangent and normal to the curve \(\frac { x^{ 2 } }{ a^{ 2 } } =\frac { y^{ 2 } }{ b^{ 2 } } =1\) at the point \((\sqrt { 2a,b } )\)

3

(a)

Find two positive numbers  whose sum is 24 and their sum of squares is minimum

3

(a)

Show that of all rectangles with a given perimeter, the square has the largest area.

3

(a)

Show that the height of the cylinder, open at the top, of given surface area and greatest volume is equal to the radius of its base.

3

(a)

A man 2 meters high walks at a uniform speed of 5km/h away from a lamp-post 6 meters high. Find the rate at which length of his shadow increases.

3

(a)