Nothing wrong with your first step.

\(\displaystyle f(x) = x(4 - x) \implies f(x) = 4x - x^2.\)

My suggestion is that you deal with the Newton quotient before you worry about the limit and go step by step. I am going to use h rather than Delta x. (Makes no difference)

So what is f(x + h)? Work it out carefully.

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Nothing wrong with your first step.

\(\displaystyle f(x) = x(4 - x) \implies f(x) = 4x - x^2.\)

My suggestion is that you deal with the Newton quotient before you worry about the limit and go step by step. I am going to use h rather than Delta x. (Makes no difference)

So what is f(x + h)? Work it out carefully.

As you can see from my working i have tried to work out f(x+h), that is little help to me. if you could properly assist with solving the equation, which will in the future help me solve alternative equations that would be great!