10 A function f with domain \(x > 0\) is such that \(\mathrm { f } ^ { \prime } ( x ) = 8 ( 2 x - 3 ) ^ { \frac { 1 } { 3 } } - 10 x ^ { \frac { 2 } { 3 } }\). It is given that the curve with equation \(y = \mathrm { f } ( x )\) passes through the point \(( 1,0 )\).
- Find the equation of the normal to the curve at the point \(( 1,0 )\).
- Find \(\mathrm { f } ( x )\).
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It is given that the equation \(\mathrm { f } ^ { \prime } ( x ) = 0\) can be expressed in the form
$$125 x ^ { 2 } - 128 x + 192 = 0$$ - Determine, making your reasoning clear, whether f is an increasing function, a decreasing function or neither.
If you use the following page to complete the answer to any question, the question number must be clearly shown.
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