For the question "Determine the equation of the tangent to the curve y = xtanx at the point with x-coordinate π." how is the answer -πx + y + π2 = 0?

Answer 1

The equation of the tangent line can be represented by the point-slope format which is y-y0=m(x-x0). The point of interest is x=pi.

Since there is no y0 coordinate provided, the tangent line equation will be in the form y=m(x-x0).

To calculate the slope(m), take the derivative of y=xtan(x) by applying the product rule, which would yield y'=m=xsec^2(x)+tan(x). Plug in pi into y' which gives pi so the value of m is pi.

Now plug everything into y=m(x-x0) -> y=pi(x-pi) -> So the equation of the tangent line is y=pix-pi^2