The Goal

Find the equation of the tangent line to

at x = 2.

The Mistake

Find the mistake:

Need a hint? Look carefully at the red part:

The Correction

An Explanation

The derivative of a function f(x) provides a formula f'(x) from which the slope of a tangent line can be computed at a point x=a by evaluating f'(x) at x=a, that is, by computing m=f'(a). The result is a number, which then can be used to find the equation of the tangent line at x=a using the point-slope form for a line, in this situation: y - f(a) = m(x-a).

(Note that in the mistaken solution the proposed tangent line equation is not the equation of a line.)