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Math · Calculus
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WWW C, please help me

Unless otherwise specified, the domain of a function fis assumed to be the set of all real numbers x for which f(x) is a real number. I. Let f(x) = 3x + x3-21x2 a) Write an equation of the line tangent to the graph of f at the point (2, -28) b) Find the absolute minimum value of f. Show the analysis that leads to your conclusion. c) Find the x-coordinate of each point of inflection on the graph of f. Show the analysis that leads to your conclusion.
43 -2 -1 0 12 345 6 Graph of j 3. A continuous function f is defined on the closed interval -4sxs6. The graph of f consists of a line segment and a curve that is tangent to the x-axis at 3, as shown in the figure above. On the interval 0x6, the function f is twice differentiable, with f(x)0. (a) Is/ differentiable at x = 0 ? Use the definition of the derivative with one-sided limits to Justify your answer. (0) For how many values of a, -4 s a < 6, is the average rate of change of f on the interval lo. 61 cqual to 0? Give a reason for your answer. (e) Is there a value of a, -4 s a < 6, for which the Mean Value Theorem, applied to the interval [a, 6) guarantees a value c, a<c<6, at which f(c) Justify your answer
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