The slope of the tangent to the curve y = f(x) at (x, f(x)) is 4 for every real number x 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 with vertex at origin and focus at (2, 0)
D.A parabola with vertex at origin and focus at (1, 0)
Explanation
Since dy/dx = 4 (constant), integrating gives y = 4x + C. The curve passes through the origin (0, 0), so C = 0, hence y = 4x. This is a straight line through the origin. At x = 1, y = 4, so the line passes through (1, 4).
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