Manipal MET2019MathematicsApplication of Derivatives

A function f(x)= x^2-3 x+2 x^2+2 x-3 is

Options

Amaximum at x=-3
Bmaximum at x=-3 and maximum at x=1
Cmaximum at x=1
Dfunction is increasing in its domain

Correct answer

D. function is increasing in its domain

Step-by-step solution

f(x)= x^2-3 x+2 x^2+2 x-3 On differentiating with respect to x , we get f^ (x)= (x^2+2 x-3 )(2 x-3)- (x^2-3 x+2 ) (2 x+2) (2 x^3+4 x^2-6 x-3 x^2-6 x+9 ) aligned & = - (2 x^3-6 x^2+4 x+2 x^2-6 x+4 ) (x^2+2 x-3 )^2 & = 5 x^2-10 x+5 (x^2+2 x-3 )^2 0 aligned = 5(x-1)^2 (x+3)^2(x-1)^2 0= 5 (x+3)^2 0 f(x) is increasing in its domain.

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