Discussion
The equation of the straight line representing the tangent to the curve \(y = x^{2}\) at the point (1,1) is
Answer: C
The tangent is y - 1 = 2(x - 1).
The slope of \(y = x^{2}\) is \(dy/dx = 2x\), which is 2 at x = 1. The point-slope form through (1,1) is therefore y - 1 = 2(x - 1), that is, y = 2x - 1.
y = 2x - 2 has the right slope but passes through (1, 0), not (1, 1). x = 2y - 1 and x - 1 = 2(y - 1) have slope 1/2, which comes from swapping x and y, the tangent to the inverse curve.
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