Question -
Answer -
The equation of the givencurve is
Differentiating with respect to x,we have:
Therefore, the slope of the tangent to thegiven curve at any point (x, y) is given by,
The given line is y = x +1 (which is of the form y = mx + c)
∴ Slope of the line = 1
The line y = x +1 is a tangent to the given curve if the slope of the line is equal to theslope of the tangent. Also, the line must intersect the curve.
Thus, we must have:
Hence, the line y = x +1 is a tangent to the given curve at the point (1, 2).
The correct answer is A.