The gradient of a curve is given by 3x\(^2\) – 8x + 2. If the curve passes through P(0, 4), find the equation of the curve.
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y = x\(^3\) - 4x\(^2\) + 2x + 4
- y = x\(^3\) - 4x\(^2\) + 2x + 2
- y = 3x\(^3\) - 4x\(^2\) + 2x + 4
- y = 3x\(^3\) - 4x\(^2\) + 2x - 2
The correct answer is: A
Explanation
The gradient of a curve is given by 3x\(^2\) - 8x + 2. P(0, 4)
\(\frac{dy}{dx}\) = 3x\(^2\) - 8x + 2
\(\int\)\(\frac{dy}{dx}\) = \(\int\)[3x\(^2\) - 8x + 2]
y = \(\frac{3x^2}{3} - \frac{8x^2}{2} + 2x + c\)
y = x\(^3\) - 4x\(^2\) + 2x + c
x = 0, y = 4
4 = \(\frac{3 \times 0^2}{3} - \frac{8 \times 0^2}{2} + 2 \times 0 + c\)
c = 4.
Thus, y = x\(^3\) - 4x\(^2\) + 2x + 4