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NEST2020MathematicsApplication of Derivatives

Let f be a twice differentiable function on R such that f(0)=1, f(1)=2, f^ (0)=-1, f^ (1)=5 and f^ (x) 0 for x [0,1] . Here, f^ (x) and f^ (x) denote the first and second order derivative of f at x respectively. Then

Options

  1. Af(x) -x+1 for x [0,1]
  2. Bf(x) 1 3 for x [0,1]
  3. Cf^ (x₁ ) f^ (x₂ ) if x₁ x₂ for x₁, x₂ [0,1]
  4. Df(x) 5 x-3 for x [0,1]

Correct answer

D. f(x) 5 x-3 for x [0,1]

Step-by-step solution

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