The tangent drawn at the point on the curve meets -axis at the point
Explanation of the correct option:
Step 1: Determine the slope of the curve
The slope of a curve at a point is obtained by differentiating the curve and substituting the value of the -coordinate of the point into the derivative.
Given curve is, .
Differentiating,
Thus, the slope of the curve at the given point is,
Step 2: Determine the equation of the tangent
The equation of the tangent can be determined by the point-slope formula which is given as,
where are the points the tangent passes through and is the slope of the tangent.
Here, as determined in the previous step.
Thus, the equation of the tangent is,
Step 3: Find the -intercept of the tangent
The -intercept of a line can be found by substituting in the equation and solving for .
Thus, the -intercept of the tangent is,
Therefore, the point at which the tangent meets the -axis is
Hence, option B is correct.