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AP EAMCET2016MathematicsApplication of Derivatives

Suppose f(x)=x(x+3)(x-2), x [-1,4] . Then, a value of c in (-1,4) satisfying f^ ( c )=10 is

Options

  1. A2
  2. B5 2
  3. C3
  4. D7 2

Correct answer

A. 2

Step-by-step solution

We have, aligned & f(x)=x(x+3)(x-2), x [-1,4] & =x (x^2+x-6 ) & f(x)=x^3+x^2-6 x aligned Differentiating w.r.f x , we get aligned & f^ (x)=3 x^3+2 x-6 & Given f(c)=10 & 3 c^2+2 c-6=10 & 3 c^2+2 c-16=0 & 3 c^2+8 c-6 c-16=0 & (3 c+8)(c-2)=0 & c=- 8 3 or c=2 & c=2 [-1,4] aligned

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