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AP EAMCET · Maths · Application of Derivatives

If f(x)=(x-1)(x-2)(x-3) for x[0,4], then the value of c(0,4) satisfying Lagrange's mean value theorem is

  1. A 3±23
  2. B 2±233
  3. C 2±32
  4. D 3±33
Verified Solution

Answer & Solution

Correct Answer

(B) 2±233

Step-by-step Solution

Detailed explanation

Given: f(x)=(x-1)(x-2)(x-3) ⇒fx=x3-6x2+11x-6 f'x=3x2-12x+11 Now, fx is continuous in R as it is a odd degree polynomial. From Lagrange's mean value theorem, if fx is continuous in a,b and differentiable in a,b then there exist c∈a,b such that f'c=fb-fab-a…