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Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 1 / 10E / a / Solution

f

is differentiable at

a

when there is a real number

L

such that

lim_{h \to 0} \frac{f ( a + h ) - f ( a ) - L h}{h} = 0.

Equivalently, the difference quotient has a finite limit, and

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

Solved by gpt-5.6-sol high.

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