For every real number x, the slope of tangent to the curve y = f(x) at (x, f(x)) is 4 and the curve passes through the origin. What is the nature of the curve?
A.A straight line passing through (1, 4)✓ Correct
B.A straight line passing through (-1, 4)
C.A parabola whose vertex is at the origin and focus at (2, 0)
D.A parabola whose vertex is at the origin and focus at (1, 0)
Explanation
Slope dy/dx = 4 (constant) means the curve is a straight line with slope 4. Integrating: y = 4x + C. Passes through origin: C = 0, so y = 4x. At x=1, y=4, so it passes through (1, 4).
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