A curve has equation $y=\mathrm{f}(x)$, where $\mathrm{f}(x)=(2 x+1)(3 x-2)^{2}$. (i) Show that $\mathrm{f}^{\prime}(x)$ can be written in the form $2(3 x-2)(p x+q)$, where $p$ and $q$ are integers.

Explanation

To find the derivative of f(x), we can use the product rule. The derivative of (2x+1) is 2 and the derivative of (3x-2)^2 is 2(3x-2)(3). Therefore, f'(x) = 2(3x-2)(3x+1), which matches the given form 2(3x-2)(px+q) where p = 3 and q = 1.

A curve has equation $y=\mathrm{f}(x)$, where $\mathrm{f}(x)=(2 x+1)(3 x-2)^{2}$. (i) Show that $\mathrm{f}^{\prime}(x)$ can be written in the form $2(3 x-2)(p x+q)$, where $p$ and $q$ are integers.

Explanation

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