Given that \(\frac{\mathrm d y}{\mathrm d x} = 3x^{2} - 4\) and y = 6
FURTHER MATHEMATICS
WAEC 2010
Given that \(\frac{\mathrm d y}{\mathrm d x} = 3x^{2} - 4\) and y = 6 when x = 3, find the equation for y.
- A. \(x^{3} - 4x - 9\)
- B. \(x^{3} - 4x + 9\)
- C. \(x^{3} + 4x - 9\)
- D. \(x^{3} + 4x + 9\)
Correct Answer: A. \(x^{3} - 4x - 9\)
Explanation
\(\frac{\mathrm d y}{\mathrm d x} = 3x^{2} - 4\)
\(y = \int (3x^{2} - 4) \mathrm {d} x = x^{3} - 4x + c\)
y = 6 when x = 3
\(6 = 3^{3} - 4(3) + c \implies 6 = 27 - 12 + c\)
\(c = 6 - 15 = -9\)
\(y = x^{3} - 4x - 9\)
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