Consider the function f(a) = - 5x + 10x + 4 on the interval - 1, 3). Evaluate this function at the endpoints of the interval. f( - 1) = f (3) = Does Rolle's Theorem apply to f on this interval? O No O Yes If Rolle's Theorem applies, find c in ( - 1, 3) such that f' (c) = 0. If Rolle's Theorem does not apply, enter "DNE". C =Let's explore the function below using the Mean Value Theorem. f(m) = (4m 12)3 There are two ac-values where the slope of the tangent line to the graph equals the slope of the secant line between a: = 0 and :1: = 9. To find them, follow the steps below. [A] First, find the slope of the secant line between a: = 0 and a: = 9. [B] Now, find the derivative of the function. fix) = [C] Set the derivative equal to mSEg and solve. One of these values is m = 0, what is the other? \"= Consider the function f(.'B) = 6 7:1:2 on the interval [ 6, 5]. Find the average or mean slope of the function on this interval, i.e. f(5)_f(_6)_ 5-(-6) By the Mean Value Theorem, we know there exists a c in the open interval ( 6, 5) such that f '(c) is equal to this mean slope. For this problem, there is only one c that works. Find it. Suppose h(t) represents the height of a projectile at time t on the time interval [0, 5] seconds. h(3) h(1) a) What does 31 represent physically (i.e. in terms of the projectile's motion). b) What does h'(c) represent physically (i.e. in terms of the projectile's motion) where 0 S c S 3 . c) What does the Mean Value theorem tell us in relation to parts a and b and in terms of the projectile's motion? Which of the following are requirements to use Mean Value Theorem for f(a) on the interval [a, b]? Choose all that apply. Of (a) is continuous on [a, b] Of (x) is differentiable on (a, b) Of (a) = f(b) Of (b ) > f (a) Da = b Of(x) is continuous on [ - co, co Of(a) is differentiable on ( - co, co)Which of the functions below meet all requirements of the Mean Value Theorem on the interval [ - 3, 3]? Choose all that apply. 0 3x2 + 12x + 5 +1 Ox-+1 O sin 4