 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2021/prelims/mathematics-ii/4/a/i/solution

f : (a, b) \to R

is differentiable on $(a, b)$ if, for every

x \in (a, b)

f^{'} (x) = h \to 0 lim \frac{f ( x + h ) - f ( x )}{h}

exists. Here

h \neq = 0

and is sufficiently small that

x + h \in (a, b)

f

x

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