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Black Book Advanced Problems in MathematicsMathematicsApplication of Derivatives

Let f be a real valued function with (n + 1) derivatives at each point of R . For each pair of real numbers a, b, a < b , such that [ f(b) + f'(b) + + f^ (n) (b) f(a) + f'(a) + + f^ (n) (a) ] = b - a **Statement-1 :** There is a number c (a, b) for which f^ (n+1) (c) = f(c) because **Statement-2 :** If h(x) be a derivable function such that h(p) = h(q) then by Rolle's theorem h'(d) = 0; d (p, q)

Options

  1. AStatement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1
  2. BStatement-1 is true, statement-2 is true and statement-2 is not correct explanation for statement-1
  3. CStatement-1 is true, statement-2 is false
  4. DStatement-1 is false, statement-2 is true

Correct answer

A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1

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