Q1) ----------------------------------------------------------------------------

ID: 2840440 • Letter: Q

Question

Q1)

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Q2)

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Q1)

f ' (t)=0

==>ue^t -ve^-t=0

==>ue^t=ve^-t

==>e^2t=v/u

==>t=0.5 ln(v/u)

Q2)f ' (x)=0

==>40xe^-0.3x -6x^2e^-0.3x=0

==>xe^-0.3x *(40-6x)=0

==>x=0, x=20/3

x=0==>f(0)=0------------>local minimum

x=20/3 ==>f(20/3)>0--->local maximum

Q3)F'(X)=0

==>8x^7 (7-x)^9 +-9x^8 (7-x)^8 =0

==>x^7 (7-x)^8 (8*(7-x) -9x)=0

==>x^7 (7-x)^8 (56-17x)=0

==>x=56/17 ,0,7

local minmum at x=0

local maximum at x=56/17 or 3.294

neither at x=7

Q4)F"(T)=0

f'(t)=4t^3+3t^2 -36t

f"(t)=12t^2 +6t -36=0

==>2t^2 +t -6=0

==>(t+2)*(2t-3)=0

==>t=-2---->smaller

, t=3/2=1.5-->larger

Q5)option A

Q6)a)g is decreasing in interval around x0

b)local minimum

c)concave up

Q7)D,F as f"(x) =0 at these points and sign of f"(x) changes

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