dse question plz help

[econ14]

q1.Consider the function f dened by f(x) =x^6 +5x^4 +2,
for all x >= 0.  The derivative of its inverse function evaluated at f(x) = 8 that is ( f^-1)'(8) equals
(a) 1/7.
(b) 1/15.
(c) 1/26.
(d) 1/20

q2.A six meter long string is cut in two pieces. The first
piece, with length equal to some x, is used to make a circle, the second, with
length(6-x),, to make a square. What value of x will minimize the sum of
the areas of the circle and the square?(x is allowed to be 0 or 6 as well).
(a) x = 24pi/(1 + 4pi).
(b) x = 6pi/(4 +pi ).
(c) x = 6.
(d) x = 1/2pi

[kangkan]

for the 1st one ,it is C..the second one is b.

[mrittik]

how do u solve it kangkan? plz solve it....

[bhavya jain]

ans 2) d)
max A= area of a circle+area of square
A=pi(x/2)^2+(6-x)^2
taking the derivative & solving for x, we'll get
x=24/pi+4
multiplying by pi in both num & denom, we get x= 24pi/ 1+4pi, so option a)

Ans 1) c)
this concept u can find in hammond.
where g'(x)=1/f'(x), thus ( f^-1)'(8) = 1/6x^5+20x^3)=1/26 [where f(1)=8, so on substituting x=1, we'll get 1/26)
 

[kangkan]

Hi bhavya..x will be the circumference hence 2pie*r=x i.e r= x/2pie.

I did the optimization with this and got the other answer 6*pie(4+pie)

[kangkan]

@mrittick and Sandeep..sorry for replying so late..i had gone to give the TERI exam

[econ14]

thanx bhavya..... can u plz give the page no. or name of the topic in hammond, I am not able to find this concept.

[kangkan]

hammond..cahpter 9 i tink..inverse functions

[ashutosh]

Approach towards q1-
Put f(x) = 8
Solve for x
x^6 +5x^4 +2 = 8
x^6 + 5 x^4 = 6
x= +- 1

Take the derivative
f'(1)= 6x^5 + 20x^3
At x=1 , f'= 26
Therefore f^-1 = 1/f' = 1/26

[ashutosh]

@bhayva
You are making a mistake in 2.

Total Area= Area of circle + Area of square
A= pi * (x2/4pi^2) +  ((6-x)/4)^2

Solving it will give answer b.