Gradient function and tangent/normal

A question is this type if and only if it requires using first principles to find a gradient, then applying this to find the equation of a tangent or normal line, possibly with further geometric calculations.

1 questions · Moderate -0.8

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OCR MEI C2 Q4
12 marks Moderate -0.8
  1. Calculate the gradient of the chord joining the points on the curve \(y = x^2 - 7\) for which \(x = 3\) and \(x = 3.1\). [2]
  2. Given that \(f(x) = x^2 - 7\), find and simplify \(\frac{f(3 + h) - f(3)}{h}\). [3]
  3. Use your result in part (ii) to find the gradient of \(y = x^2 - 7\) at the point where \(x = 3\), showing your reasoning. [2]
  4. Find the equation of the tangent to the curve \(y = x^2 - 7\) at the point where \(x = 3\). [2]
  5. This tangent crosses the \(x\)-axis at the point P. The curve crosses the positive \(x\)-axis at the point Q. Find the distance PQ, giving your answer correct to 3 decimal places. [3]