Answer: Show that f(0) = 0^4 − 0 = 0 and that f(1) = 1^4 − 1 = 0.
Next, find f′(x) = 4x^3 − 1. By setting f′(c) = 4c^3 − 1 = 0 and solving, you’ll see that c = , which is in
the interval.
PRACTICE PROBLEM SET 9
Now try these problems. The answers are in Chapter 19.
1.Find the values of c that satisfy the MVTD for f(x) = 3x^2 + 5x − 2 on the interval [−1, 1].2.Find the values of c that satisfy the MVTD for f(x) = x^3 + 24x − 16 on the interval [0, 4].3.Find the values of c that satisfy the MVTD for f(x) = − 3 on the interval [1, 2].4.Find the values of c that satisfy the MVTD for f(x) = − 3 on the interval [−1, 2].5.Find the values of c that satisfy Rolle’s Theorem for f(x) = x^2 − 8x + 12 on the interval [2, 6].6.Find the values of c that satisfy Rolle’s Theorem for f(x) = x(1 − x) on the interval [0, 1].7.Find the values of c that satisfy Rolle’s Theorem for f(x) = 1 − on the interval [−1, 1].- Find the values of c that satisfy Rolle’s Theorem for f (x) = on the interval [0, 1].