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1.9.20 Integrate kx^n

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Question 13

A curve C C\,C has equation y=f(x)y = f(x)y=f(x), x>0x > 0x>0.

Given that

  • f′′(x)=6x−1x2f''(x) = 6x - \dfrac{1}{x^2}f′′(x)=6x−x21​
  • the point P P\,P has xxx-coordinate 1 and lies on CCC
  • the tangent to C C\,C at P P\,P has equation y=5x−3y = 5x - 3y=5x−3
a.

Find an equation of the normal to C C\,C at PPP.

[4]
b.

Find f(x)f(x)f(x), writing your answer in simplest form.

[6]

1.9.20 Integrate kx^n Questions

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