Question

Find the equation of the tangent line to f(x)=x sec x at (pi/4, pi •sqrt of 2 all over 4).

I got to here, but did not know what to do next:

slope: (pi/4)(sqrt of 2 over 2) + (sqrt of 2 over 2) everything over 1/2=.......

Answer 1

y = x secx , point is (π/4 , π√2/4)

dy/dx = x secx tanx + secx
= secx(x tanx + 1)
so at the given point:
slope = √2( (π/4)(1) + 1) = π√2/4 + √2

so using y = mx + b
π√2/4 = (π√2/4 + √2)(π/4) + b

solve this mess for b and you are done

Answer 2

looks good to me

http://www.wolframalpha.com/input/?i=plot+y+%3D+xsecx%2C+y+%3D+%28%CF%80%E2%88%9A2%2F4+%2B+%E2%88%9A2%29x+%2B+%CF%80%E2%88%9A2%2F4+-+%28%CF%80%E2%88%9A2%2F4+%2B+%E2%88%9A2%29%28%CF%80%2F4%29