The tangent of the curve at has gradient
Explanation for the correct option:
Step 1: Differentiate the given curve
Given,
The slope of the tangent of a curve is described by its derivative.
The derivative of the given function is,
Step 2: Evaluate the derivative at
To evaluate the gradient of a function at a given point, we have to substitute the value of the -coordinate at the point into the derivative of the function.
But directly substituting yields indeterminate form. Thus, we have to take the limit of the derivative at .
Thus,
Applying L'Hospital's rule,
Hence, option A is correct.