A student attempts to differentiate f(x)=4xf(x)=4xf(x)=4x from first principles and writes f′(x)=limh→04(x+h)−4xxf'(x)=\displaystyle\lim_{h\to0}\dfrac{4(x+h)-4x}{x}f′(x)=h→0limx4(x+h)−4x.
Identify the error and complete a correct first-principles derivation.
8 exam-style questions on OCR (MEI) A Level Maths 1.9.2 Gradient as limit of chord gradient. Each one has a worked solution and a mark scheme showing where the marks go.