Round your answers to two digits. Consider the following function H(s, t) = 5. t2 - 6. $5. This is a multi-part question, asking you to find both the linear approximation to this function and the linear approximation to a level curve of this function. 1. At (so, to), H(so, to) = -187. We are told to = 1. Find so . In other words, solve H(so, 1) = -187 for so . Answer: So 2. Find the linear approximation for H (s, t) in proximity of (so, to) and express it as H(s, t ) ~ atb . (s - p) + c. (t - q) . The coefficient a is equal to . The coefficient b is equal to o The coefficient c is equal to 3. Next, consider the level curve H(s, t) = -187. It implicitly defines t as a function of s. Find the point at which t( s ) = 1. Answer: S =4. Find the first derivative of t with regard to s along the level curve and express it as: t' = a . s'tc + d . st + g . In(s + t) +k. o The coefficient a is equal to . The coefficient b is equal to . The coefficient c is equal to The coefficient d is equal to . The coefficient g is equal to . The coefficient k is equal to 5. Find the second derivative of t with regard to s along the level curve and express it as: t" = 12 . sato - c . sat9 + k . east. The coefficient a is equal to . The coefficient b is equal to o The coefficient c is equal to . The coefficient d is equal to The coefficient g is equal to o The coefficient k is equal to6. Find the linear approximation for t(s) in proximity of so and express it as t( s) ~ atb. (s - p) + c. (t- q) o The coefficient a is equal to o The coefficient b is equal to o The coefficient p is equal to . The coefficient c is equal to The coefficient q is equal to