What is the nature of the curve?
Consider the following for the two (02) items that follow : 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.
- A. A straight line passing through (1, 4) ✓
- 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)
Correct Answer: A. A straight line passing through (1, 4)
Explanation
The slope of the tangent is given by \frac{dy}{dx} = 4. Integrating both sides gives y = 4x + C. Since the curve passes through the origin (0,0), C = 0. The equation is y = 4x, which is a straight line. It passes through (1, 4) because 4 = 4(1).
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