The gradient of point P on the curve \(y = 3x^{2} - x + 3\)
FURTHER MATHEMATICS
WAEC 2009
The gradient of point P on the curve \(y = 3x^{2} - x + 3\) is 5. Find the coordinates of P.
- A. (1, 5)
- B. (1, 7)
- C. (1, 13)
- D. (1, 17)
Correct Answer: A. (1, 5)
Explanation
\(y = 3x^{2} - x + 3\)
\(\frac{\mathrm d y}{\mathrm d x} = 6x - 1 = 5\)
\(6x = 5 + 1 = 6 \implies x = 1\)
\(y = 3(1^{2}) - 1 + 3 = 3 - 1 + 3 = 5\)
\(P = (1, 5)\)
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