Let f(x)=x 2
−10x+12 Find the critical point c of f(x) and compute f(c). The critical point c is = The value of f(c)= Compute the value of f(x) at the endpoints of the interval [0,10]. f(0)= f(10)= (1 point) Consider the function f(x)=7−2x 2
on the interval [−2,3]. (A) Find the average or mean slope of the function on this interval, i.e. 3−(−2)
f(3)−f(−2)
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= (B) By the Mean Value Theorem, we know there exists a c in the open interval (−2,3) such that f ′
(c) is equal to this mean slope. For this problem, there is only one c that works. Find it. c= (1 point) Suppose f(x) is continuous on [4,6] and −4≤f ′
(x)≤3 for all x in (4,6). Use the Mean Value Theorem to estimate f(6)−f(4). Answer: ≤f(6)−f(4)≤