Case study Chapter 6 ( Application of derivative )

Case study 1: Read the following and answer the question(Case study application of derivative 1 )
A recangular hall is to be developed for a meeting of farmers in an agriculture college to aware them for new technique in cultivation. It is given that the floor has a fixed perimeter P as shown below.

(i) If x and y represents the length and breadth of the rectangular region, then the relation between the variables is

(a) x + y = P               (b) x² + y² = P

(b) 2(x + y) = P          (d) x + 2y =P

(ii) The area of rectangular region ‘A’ expressed as a function of x is

(a) 1/2(P + x²)            (b) 1/2(Px – 2x²)

(c) 1/2(Px + 2x²)         (d) Px – 2x²

(iii) Principal of agriculture college is interested in maximizing the area of floor ‘A’. For this to happen the value of x should be

(a) P                               (b) P/2

(c) 2P/3                         (d) P/4

(iv) To maximizing the area of floor ‘A’. For this to happen the value of y should be

(a) P/2                           (b) P/4

(c) P/3                            (d) 2P/5

(v) The maximum value of area of floor ‘A’ is

(a) P²/8                         (b) 2P/9

(c) P/10                           (d) P²/16

Perimeter of triangle ABCD = 2(l + b)

=  2(x + y)

Since,

A = x.y

Since,

For maximum or minimum value of x

Also,

Putting x = P/4 in y = (P-2x)/2

Since A = length × breadth

= x × y

Some other Case study

Case study 2:- Read the following and answer the question.(Case study application of derivative 2)

Dr. Ritam residing to Delhi went to see an apartment of 3 BHK in Noida. The window of the house was in the form of a rectangle surmounted by a semicircular opening having a perimeter of the window 10 m as shown in figure.

Case study 3:- Read the following and answer the question:(Case study application of derivative 3)

On the request of villagers, a construction agency designs a tank with the help of an architect. Tank consist of rectangular base with recangular sides, open at the top so that its depth is 2 m and volume is 8 cubic meter as shown below:

Case study 4:- Read the following and answer the question:(Case study application of derivative 4 )

These days chinese and Indian troops are engaged in aggressive melee,face-off skirmishes at location near the disputed Pangong Lake in Ladakh.

One day a helicopterof enemy is flying along the curve represented by y = x² + 7. A soldier placed at (3, 7) wants to shoot down the helicopter when it is nearest to him.