Calculus
please answer the following problems
( final result only is okay )
Section 4.1: Problem 2 (1 point) Previous Problem Problem List Next Problem Find all critical values for the function f(r) = 972 + 10 and then list them (separated by commas) in the box below. List of critical numbers:Section 4.1: Problem 6 (1 point) Previous Problem Problem List Next Problem Find the absolute maximum and absolute minimum values of the function f(x) = (x -2)(x -5)3+10 on each of the indicated intervals. Enter 'NONE' for any absolute extrema that does not exist. (A) Interval = [1, 4]. Absolute maximum = Absolute minimum = (B) Interval = [1, 8]. Absolute maximum = Absolute minimum = (C) Interval = [4, 9]. Absolute maximum = Absolute minimum =Section 4.1: Problem 7 (1 point) Previous Problem Problem List Next Problem -I Consider the function f(I) = 6:x2 +1 This function has an absolute minimum value equal to: which is attained at I and an absolute maximum value equal to: which is attained at ~ =Section 4.1: Problem 8 {1 point] Previous Problem Problem List Next Problem Find the absolute maximum and absolute minimum values of the function z} =33+ 12::2 2?: +9 over each of the indicated intervals. {a} Interval = [1D,IJ]_ 1. Absolute maximum 2. Absolute minimum {b} Interval = [T, 2]. 1. Absolute maximum 2. Absolute minimum [o] Interval = [11], 2]. 1. Absolute maximum 2. Absolute minimum Section 4.2: Problem 1 (1 point) Previous Problem Problem List Next Problem Consider the function f(x) =5 - 5x2 on the interval [-1, 6]. Find the average rate of change of the function on this interval, i.e. f(6) - f(-1) 6 - (-1) By the Mean Value Theorem, we know there exists a c in the open interval (-1, 6) such that f'(c) is equal to this average rate of change. For this problem, there is only one c that works. Find this value of c. C =Section 4.2: Problem 2 {1 point) Previous Problem Problem List Next Problem Consider the function x) 2 i on the interval [4,11]. Find the average rate of change of the function on this interval. C] Ely the Mean Value Theorem, we know there exists a c in the open interval (4, 11} such that f'((:) is equal to this average rate of change. For this problem, there is only one at: that works. Find this value of c. c=j Section 4.2: Problem 3 [1 point) Previous Problem Problem List Next Problem Consider the function j[z)=23322+4z4 Find the average rate of change of this function on the interval [1, 7). E] Ely the Mean Value Theorem, we know there exists a c in the open interval (1, T} such that 3'16} is equal to this average rate of change. Find the value of C in the interval which works E] Section 4.2: Problem 4 (1 point) Previous Problem Problem List Next Problem Consider the function f(r) = 2 - 4x + 5 on the interval [0, 4]. Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval. f(x) is on [0, 4]; f(x) is on (0, 4); and f(0) = f(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 =:Section 4.2: Problem 5 {1 point) Previous Problem Problem List Next Problem Suppose x} is continuous on [2, 8] and 2 <_: g for all z in use the mean value theorem to estimate b h2 answer: d section problem point previous list next does there exist a continuous function f such that and x v yes or no>
