1. 

Suppose f(x) is continuous on [a,b]. The average value of the function f(x) on the interval [a,b] is Suppose f(x) is continuous on its domain [a,b]. The Mean Value Theorem for Integrals tells us that there is a number c in (a,b) such that f(c) is equal to O the maximum of the function f(x) 0 the derivative of the function f(x) 0 the integral of the function f(x) 0 the slope of the tangent line of f(x) at c O the average value of f(x) \fIn a certain city the temperature (in F) t hours after 9 AM was modeled by the function T(t) = 50 + 13 sin(). 12 Find the average temperature Tave during the period from 9 AM to 9 PM. (Round your answer to the nearest whole number.) Tave = |:| F Consider the given function and the given interval. f(x) = (x - 6)2, [5, 8] (a) Find the average value fave of f on the given interval. fave = 1 (b) Find c such that fave = f(c). C = (smaller value) C = (larger value)Find the linear approximation of the function f(x) = \\ 4 - x at a = 0. L( X ) = Use L(x) to approximate the numbers v 3.9 and v 3.99. (Round your answers to four decimal places.) 3.9 ~ 3.99 ~Suppose that we don't have a formula for 900 but we know that 9(3) = 3 and g'(x) = x2 + 7 for all x. (8) Use a linear approximation to estimate g(2.99) and g(3.01)