Determine the equation of the tangent line to the function (² = square): f(x) = x + cos²x at x = pie/4

Answer 1

f'(x) = 1+ 2cosx(-sinx)

f(π/4) = π/4 + cos^2 (π/4) = π/4 + 1/2 = (2+π)/4
f'(π/4) = 1 + 2(1/√2)(-1/√2) = 1 - 2/2 = 0

so the line is horizontal and its equation is simply
y = (2+π)/4

check my arithmetic, (did not write it down first)

Answer 2

Thanks Reiny, I have checked it over and it seems about right to me. Thank you.