- In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
- Find the equation of the tangent to the curve with equation
$$y = \frac { 1 } { 4 } x ^ { 3 } - 8 x ^ { - \frac { 1 } { 2 } }$$
at the point \(P ( 4,12 )\)
Give your answer in the form \(a x + b y + c = 0\) where \(a\), \(b\) and \(c\) are integers.
The curve with equation \(y = \mathrm { f } ( x )\) also passes through the point \(P ( 4,12 )\)
Given that
$$f ^ { \prime } ( x ) = \frac { 1 } { 4 } x ^ { 3 } - 8 x ^ { - \frac { 1 } { 2 } }$$ - find \(\mathrm { f } ( x )\) giving the coefficients in simplest form.