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AP EAMCET201921 Apr 2019Morning ShiftMathematicsQuadratic EquationActual

Let f(x)=x^2+2 x+2, g(x)=-x^2+2 x-1 and a, b be the extreme values of f(x), g(x) respectively. If c is the extreme value of f g (x) (for x 1 ), then a+2 b+5 c+4=

Options

  1. A2
  2. B1
  3. C4
  4. D3

Correct answer

C. 4

Step-by-step solution

Given, aligned f(x) & =x^2+2 x+2 & =x^2+2 x+1+1=(x+1)^2+1 aligned Here, f(x) aligned & [1, ) and g(x)=-x^2+2 x-1 & =- (x^2-2 x+1 )=-(x-1)^2 aligned Here, g(x) (- , 0] Now, f g (x)= x^2+2 x+2 -x^2+2 x-1 =y array ll & x^2+2 x+2=-y x^2+2 x y-y & x^2+y x^2+2 x-2 x y+2+y=0 & x^2(1+y)+(2-2 y) x+2+y=0 & D 0 & (2-2 y)^2-4(2+y)(1+y) 0 & 4+4 y^2-8 y-4(2+y)(1+y) 0 & 1+y^2-2 y-(2+y)(1+y) 0 & 1+y^2-2 y- (2+2 y+y+y^2 ) 0 & 1+y^2-2 y-2-3 y-y^2 0 & -5 y-1 0 & y - 1 5 array So, f g (x) (- ,- 1 5 ] So, a=1, b=0 and c=- 1 5 Hence, al

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