Find the linearization off (x) =x^(sinx) at a=3π/2

Answer 1

f(3π/2) = - 3π/2

By product rule, f^'(x) = sinx +xcosx

f^'(3π/2) = - 1

Local linearization (aka eqn of the tangent line) = y + 3π/2 = - (x - 3π/2) or y = - x