Need answer to the following question.
We first find the slope of the tangent for which we need derivative of f(x). Differentiating f(x) w.r.t. x we get:
Now, slope is the value of f’(x) at the given point x = 1.
Now, to find any one point on the tangent line, we consider the fact that tangent line is drawn at x=1. This point also lies on the curve and hence its y-coordinate is the value of f(x) at x=1. We get:
Equation of a line in slope-point form is given as, (y – y1) = slope * (x – x1). Substituting the values of slope, x1 and y1, we get:
Answer: The equation of tangent line to the given curve at x = 1 is: