Doubts

[Rautparul]

Thanks.

[Rautparul]

ISI 2016

15. The solution of the optimization problem
max 3xy − y3
x,y
subject to
2x + 5y ≥ 20
x − 2y = 5
x, y ≥ 0.

is given by:

(a) x = 19, y = 7.
(b) x = 45, y = 20.
(c) x = 15, y = 5.
(d) None of the above

[Rautparul]

 Let f : R → R be a strictly increasing function. Let g be the inverse of the function f. If f′(1) = g(1) = 1, then g′(1) equals to
(a) 0.
(b) 1/2
(c) −1.
(d) 1.

[Abhitesh]

g'(1)= g(1+h)-g(1)/h

Now f(1+h)=f(1) + f'(1)h = 1+h
=>f-1(1+h) = 1+h = g(1+h)
=>g'(1) = 1

[Rautparul]

Thanks Abhitesh. Did you get optimisation problem? I had a hard time doing it!! Didn't get the solution.

[Abhitesh]

Q4.pdf