First principles: polynomial (find gradient)

A question is this type if and only if it asks students to use differentiation from first principles to find the gradient or derivative of a polynomial at a specific point or in general, without the answer being given.

2 questions · Moderate -0.5

1.07g Differentiation from first principles: for small positive integer powers of x
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Edexcel Paper 1 Specimen Q9
5 marks Moderate -0.5
  1. The curve \(C\) has equation
$$y = 2 x ^ { 3 } + 5$$ The curve \(C\) passes through the point \(P ( 1,7 )\).
Use differentiation from first principles to find the value of the gradient of the tangent to \(C\) at \(P\).
OCR PURE Q4
5 marks Moderate -0.5
4 The quadratic polynomial \(2 x ^ { 2 } - 3\) is denoted by \(\mathrm { f } ( x )\).
Use differentiation from first principles to determine the value of \(\mathrm { f } ^ { \prime } ( 2 )\).