1. Consider the function f (x) =x² – 4x + 6 on the interval [0,4]. Verify that this function satis-fies thethree hypotheses of Rolle's Theorem on the inverval.f(x) is.f(x) is.and f(0) = f(4) =..on [0,4];on (0,4);Then by Rolle's theorem, there exists at least one value c such that f'(c) = 0. Find all such values c andenter them as a comma-separated list.Values of c =:.Answer(s) submitted:(incorrect)2. Suppose f (x) is continuous on [4, 8] and –2 4. Consider the function f (x) = 6 – 7x²on the interval [-1,5].(A) Findthe average or mean slope of the function on this interval, i.e.f(5) – f(-1)5-(-1)(B) By the Mean Value Theorem, we know there exists a c in the open interval (-1,5) such that f'(c) isequal to this mean slope. For this problem, there is only one c that works. Find it.Answer(s) submitted:(incorrect)5. Let f(x) = 3 sin(x).a.) [f"(x)| <.b.) By the Mean Value Theorem, |f(a) – f(b)|<–la– b| for all a and b.Answer(s) submitted:(incorrect)6. Suppose that f (0) = 1 and f'(x) <7 for all values of x. Use the Mean Value Theorem to determinehow large f (4) can possibly be.Answer: f(4) <.Answer(s) submitted:(incorrect)7.Consider the function f(x) =} on the interval [1,11].(A) Find the average or mean slope of the function on this interval.Average Slope =(B) By the Mean Value Theorem, we know there exists a c in the open interval (1,11) such that f'(c) isequal to this mean slope. Find all values of c that work and list them (separated by commas) in the boxbelow.List of values:Answer(s) submitted:(incorrect)8.Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function.If there are multiple values, separate them with commas; enter N if there are no such values.f(x) = x² – Lx+5, [0, 1]

1. Step 1: Hello. Since you have posted multiple questions and not specified which question…

1. Consider the function f (x) =x² – 4x + 6 on the interval [0,4]. Verify that this function satis-fies the three hypotheses of Rolle's Theorem on the inverval. f(x) is. f(x) is. and f(0) = f(4) =. .on [0,4]; on (0,4); Then by Rolle's theorem, there exists at least one value c such that f'(c) = 0. Find all such values c and enter them as a comma-separated list. Values of c =:. Answer(s) submitted: (incorrect) 2. Suppose f (x) is continuous on [4, 8] and –2