## Question

###### 6 pts) Another way to express the curvature of & plane curve y = f(z) is given by the formulaIf" ()|n(x) [1 +(f'(2))21372 Use that equation to prove that the curvature at an inflection point of f is 0.4. (12 pts) Let u(t) = fi(t)i + fz(t)j + fs(t)k and v(t) = 9(t)i + g2(t)j + gs(t)k; and let f(t) be a real valued continuous funetion Use the definition of the derivative of a vector function (s0__a limit) to prove the following differentiation rulcs:#[u(t) + v(t)] u' (t) +v(t)

6 pts) Another way to express the curvature of & plane curve y = f(z) is given by the formula If" ()| n(x) [1 +(f'(2))21372 Use that equation to prove that the curvature at an inflection point of f is 0. 4. (12 pts) Let u(t) = fi(t)i + fz(t)j + fs(t)k and v(t) = 9(t)i + g2(t)j + gs(t)k; and let f(t) be a real valued continuous funetion Use the definition of the derivative of a vector function (s0__a limit) to prove the following differentiation rulcs: #[u(t) + v(t)] u' (t) +v(t) #[f(t)u(t)] f'(t)u(t) + f(t)u'(t)

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