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Year 12 Maths Advanced (2027) Applications of calculus

Differentiability & Continuity

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Questions
Question 1
188649
A function \(f\) is differentiable at \(x=a\) if:
A.
\(\displaystyle\lim_{h\to 0}\dfrac{f(a+h)-f(a)}{h}\) exists
B.
\(f(a)=0\)
C.
\(f(a)\) exists
D.
the curve crosses the \(x\)-axis at \(a\)
\(\displaystyle\lim_{h\to 0}\dfrac{f(a+h)-f(a)}{h}\) exists

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