Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.8

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12th ICSE

IMPORTANT

Earn 100

Find the maximum profit that a company can make, if the profit function is given by $p (x) = 41 + 72 x - 18 x^{2}$

Important Questions on Applications of Derivatives

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12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.8

The cost (in Rs.) per article

C

of manufacturing a certain article is given by the formula

C = 5 + \frac{48}{x} + 3 x^{2}

, where

x

is the number of articles manufactured per hour. Find the minimum value of

C

.

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.8

Prove that of all the rectangles with given area, the square has the smallest perimeter.

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.8

Of all rectangles each of which has perimeter

24 c m

, find the one having maximum area. Also find that area.

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.8

Prove that all rectangles with given perimeter, the square has the largest area.

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.8

Prove that the perimeter of the right angled triangle of a given hypotenuse is maximum when the triangle is isosceles.

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12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.8

Two sides of a triangle have length

a

and

b

and the angle between them is

θ

. What value of

θ

will maximise the area of the triangle? Also find the maximum area of the triangle.

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.8

A right-angled triangle with constant area is given. Prove that the hypotenuse of the triangle is least when the triangle is isosceles.

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.8

The lengths of the sides of the triangles are $9 + x^{2}$ , $9 + x^{2}$ and $18 - 2 x^{2}$ . Calculate the area of the triangle in terms of $x$ .