1. Let f be a differentiable scalar-valued function defined on an open subset of R". Sup- pose 5: R + R" has the property that flo(t)) = c for all t for some constant c. Prove that (1) o(t)) is orthogonal to '(t) for all t. (Note: this problem proves that the gradient of a function is orthogonal to its level sets) 1. Let f be a differentiable scalar-valued function defined on an open subset of R". Sup- pose 5: R + R" has the property that flo(t)) = c for all t for some constant c. Prove that (1) o(t)) is orthogonal to '(t) for all t. (Note: this problem proves that the gradient of a function is orthogonal to its level sets)