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AP EAMCET2008MathematicsApplication of Derivatives

If m and M respectively denote the minimum and maximum of f(x)=(x-1)^2+3 for x [-3,1] , then the ordered pair (m, M) is equal to

Options

  1. A(-3,19)
  2. B(3,19)
  3. C(-19,3)
  4. D(-19,-3)

Correct answer

B. (3,19)

Step-by-step solution

Given that, f(x)=(x-1)^2+3, x [-3,1] On differentiating w.r.t. x , we get f^ (x)=2(x-1) For maxima and minima, put f^ (x)=0 aligned & & 2(x-1) & =0 & & x & =1 aligned Now, f^ (x)=2 , minima x R At x=1 , f(1)=(1-1)^2+3=3 At aligned x & =-3, f(-3) & =(-3-1)^2+3=19 aligned Here, m=3 and M=19 Hence, required ordered pair is (3,19)

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