For a function $f$ with domain $x > 0$, the derivative is given by $f'(x) = 8(2x - 3)^{\frac{1}{3}} - 10x^{\frac{2}{5}}$. The curve $y = f(x)$ is stated to pass through the point $(1, 0)$.
(a)[3]
Find the equation of the normal at the point $(1, 0)$ on the curve.
(b)[4]
Find $f(x)$.
(c)[3]
It is given that the equation $f'(x) = 0$ can be rewritten as $125x^2 - 128x + 192 = 0$. Determine, making your reasoning clear, whether $f$ is an increasing function, a decreasing function or neither.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Hence $f'(1)=-18$” …