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.46/1.42 Points] DETAILS PREVIOUS ANSWERS SCALC9 3.2.EI.001. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Review the Explore It, then use it to complete the exercise below. EXPLORE IT X CONCEPT EXPLORE & TEST WHEN WOULD I USE THIS YOU WILL LEARN ABOUT: The Mean Value Theorem for Derivatives. speed limit = 50 mph secant line, 40- slope = 60 mph Position (miles tangent lines with O slope = 60 mph 025 05 0.75 Time (hours) In the diagram above, imagine an officer noting the time in which an individual enters and exits a toll road (via the time stamps on the receipts or stubs). The officer could issue a ticket based on the Mean Value Theorem if the ratio of the distance traveled (f(b) - f(a)) to the travel time (b - a) is greater than the speed limit. The MVT states that at some point between a and b, the slope of the graph (the speed of the car at an instant) must be equal to the slope of the secant line through the endpoints. In other words, there must be some c in the interval (a, b) such that f' (c) = [(b) -f(a) Click here to access the Explore It in a new window. Select Scenario 1, which is about polynomials. Change the function to f(x)= -3 - x + x3 and set the interval being considered to [-1, 1]. two points through, which the secant line is drawn are (a, f(a)) = (-1, 0 x ) and (b, f(b)) = (1,10 x The slope of the secant line is 0 . This means the secant line is horizontal (c) From left to right and to the nearest hundredth, the values of c that satisfy the conclusion of the Mean Value Theorem in this case are c, = 0 x and c2 = 0 x