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KVPY2010MathematicsApplication of Derivatives

The following figure shows the graph of a differentiable function y = f ( x ) on the interval [ a , b ] (not containing 0 ). Let g(x)=f(x) / x which of the following is a possible graph of y=g(x) ?

Options

  1. AFig. 1
  2. BFig. 2
  3. CFig. 3
  4. DFig. 4

Correct answer

B. Fig. 2

Step-by-step solution

array l f^ (c)=0 f^ (c⁻ )>0 f^ (c⁺ ) < 0 g(x)= f(x) x g^ (x)= x f^ (x)-1 x² g^ (c⁺ )= _ h 0 (c+h) f^ (c+h)-1 (c+h)² < 0 (f^ (c+h) < 0 ) array hence fig.(2)

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