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Let f: R²R be a C¹ function and consider the smooth paths c(t) = (sin(t), cos(t)) for t = [0, 2π), d(t) = (0, 1) + (-1,0
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Let f: R²R be a C¹ function and consider the smooth paths c(t) = (sin(t), cos(t)) for t = [0, 2π), d(t) = (0, 1) + (-1,0
Let f: R²R be a C¹ function and consider the smooth paths c(t) = (sin(t), cos(t)) for t = [0, 2π), d(t) = (0, 1) + (-1,0) for t € [1,1]. Define the compositions h₁ (t) = f(c(t)), h₂(t) = f(d(t)). Justify the equation h₁ (0) = h'₂ (0) and find a unit vector u and a point a E R2 such that Daf(a)=h(0) = h'₂ (0).