1.7 Integration

A curve has equation $y = f (x)$ , where

\frac{12}{\sqrt{x^5}} + 4x, \quad x > 0

The point $P (1, - 2)$ lies on the curve.

Given that $f^{'} (x) = 1$ at point $P$ ,

a.

find the equation of the normal at $P$ , writing your answer in the form $y = m x + c$ , where $m$ and $c$ are constants,

[3]

b.

find $f (x)$ .

[5]

A curve has equation $y = f (x)$ , where

\frac{12}{\sqrt{x^5}} + 4x, \quad x > 0

The point $P (1, - 2)$ lies on the curve.

Given that $f^{'} (x) = 1$ at point $P$ ,

a.

find the equation of the normal at $P$ , writing your answer in the form $y = m x + c$ , where $m$ and $c$ are constants,

[3]

b.

find $f (x)$ .

[5]

1.7 Integration Questions