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NDA2017MathematicsContinuity and DifferentiabilityActual

If F(x)= 9-x^2 , then what is _ x 1 F(x)-F(1) x-1 equal to?

Options

  1. A- 1 4 2
  2. B1 8
  3. C- 1 2 2
  4. D1 2 2

Correct answer

C. - 1 2 2

Step-by-step solution

_ x 1 F(x)-F(1) x-1 We know, _ x a F(n)-F(a) x-a =F^ (a) aligned & F^ (x)= d d x ( 9-x^2 ) & = 1(0-2 x) 2 9-x^2 = -x 9-x^2 & F^ (1)= -1 9-1 = -1 8 = -1 2 2 aligned

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