(7) Let f: R + R be a Cl function. Recall from HW3 Q.8 that the graph of f is the surface M := {(x, f(x)) R" XR | 2 R"} g(x, z) = f(x) z. Now, given a point p := (20, f(x)) M on the surface M, prove that T M = Tp. Here To = (span{ Vg(P)})+ is the in R" x R and that M can also be described as the zero set of 3 T-space at p. Hint: here you are allowed to use the fact that at a regular point the tangent space and the T-space are equal. (7) Let f: R + R be a Cl function. Recall from HW3 Q.8 that the graph of f is the surface M := {(x, f(x)) R" XR | 2 R"} g(x, z) = f(x) z. Now, given a point p := (20, f(x)) M on the surface M, prove that T M = Tp. Here To = (span{ Vg(P)})+ is the in R" x R and that M can also be described as the zero set of 3 T-space at p. Hint: here you are allowed to use the fact that at a regular point the tangent space and the T-space are equal