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JEE Main2004MathematicsApplication of DerivativesActual

A function y=f(x) has a second order derivative f^ (x)=6(x-1) . If its graph passes through the point (2,1) and at that point the tangent to the graph is y=3 x-5 , then the function is

Options

  1. A(x-1)^2
  2. B(x-1)^3
  3. C(x+1)^3
  4. D(x+1)^2

Correct answer

B. (x-1)^3

Step-by-step solution

f^ (x)=6(x-1) f^ (x)=3(x-1)^2+c and f^ (2)=3 c=0 f(x)=(x-1)^3+k and f(2)=1 k=0 f(x)=(x-1)^3

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