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The function f that satisfies f'(x) = 3x2 +1, f(2)=5 is Select one: a. f(2)=23+ O b. f(x) = 2 + 1 - 5 O c. f(x)=x3 ++2 d. f(x) = 3x2 – 7 O e. None of these. Let f(2) be a function that is continuous on 1, 7] with f(1) =3 and f(7) = 9. Then the Intermediate Value Theorem guarantees that Select one: O a. f'(2)=1 has at least on solution in the open interval (1,7). O...
Consider the following. f(x) = 1 4 x4 + 1 2 x3 − 3x2 + 4 Find f '(x). f '(x) = x3+ 3x2 2−6x Find f ''(x). f ''(x) = 3x2+3x−6 Find the x-values of the possible points of inflection. (Enter your answers as a comma-separated list.) x = Determine the intervals on which the function is concave up. (Enter your answer using interval notation.) Determine the intervals on which the function is concave down. (Enter your answer using...
Find the ABSOLUTE MAXIMUM value of the function f(x) = – x3 + 3x2 - 4 on the closed interval [ – 2,1]. 1A - 4 B. o C-1 D. -2 E 16
(4) Using the intermediate value theorem, determine, if possible, whether the function f has at least one real zero between aandb. f(x)= 3x2 - 2x -11;a=2,6 = 3 (b) Graph the polynomial (a)P(x) = 2(x + 2)(x - 1)(x – 3)
a) determine the area bounded by the graph of
f(x)=3x2 and the x axis between x=0 and x=1
b) evaluate intergral
2.0 – 2 -do C2 - 2.0
Consider the following. f(x) = - *** + 3x3- 1/3 - 3x2 + 8 Find f'(x). f'(x) = Find F"(x). f"(x) = Find the x-values of the possible points of inflection. (Enter your answers as a comma-separated list.) X = Determine the intervals on which the function is concave up. (Enter your answer using interval notation.) Determine the intervals on which the function is concave down. (Enter your answer using interval notation.) Locate the points of inflection. (If an answer...
3. Let X; - x2 + x3 = 0 for parts (a) and x + 3X2 = 0 2X - 2x2 + 3x3 =0 . (b) below: a) Find the determinant of b) Does the system of equations have a solution ? If yes, what is it?
3. (12 pts) Find the absolute maximum and absolute minimum of f(x) x3 3x2-9x -4 on the interval [0, 4]. 12 AT 4. (10 pts) Sketch the graph of a function f(x) which has the following characteristics: (2) 1, f(5) 5, lim f(), i f)1, m끊f(x)-1, and limo f(x) = 4.
3. (12 pts) Find the absolute maximum and absolute minimum of f(x) x3 3x2-9x -4 on the interval [0, 4]. 12 AT 4. (10 pts) Sketch the graph of...
(11) Does the function f(x) = 3x2 + 5x – 2, defined for r € (-1, 1), satisfy the hypotheses of the Mean Value Theorem? Find x = c such that f'(c) is the slope of the secant line passing through (-1,f(-1)), and (1, f(1)).
For the polynomial below, 3 is a zero. g(x) = x3 + 3x2 – 5x - 39 Express g (x) as a product of linear factors. 8(x) = 0 x 5 ? Find all other zeros of P(x) = x + x + 4x + 30, given that 1 – 3i is a zero. (If there is more than one zero, separate them with commas.) x 6 ? The figure below shows the graph of a rational function f. It...