4MA1/1H Jan 2022, Question 24: Gradient of a Curve at a Point
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 6 marks
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The question, in short
Curve y = ax³ + bx² − 12x + 6 passes through (2, −6) with gradient 16 there; find constants a and b, then the y value at x = 3.
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Solution · 6 marks
- 1A on C: 8a + 4b − 24 + 6 = −6, so 8a + 4b = 12
- 2dy/dx = 3ax² + 2bx − 12; at x = 2: 12a + 4b − 12 = 16, so 12a + 4b = 28
- 3Subtract: 4a = 16, so a = 4 and b = −5
- 4At x = 3: y = 4(27) − 5(9) − 12(3) + 6 = 108 − 45 − 36 + 6 = 33
Answer33
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