Given the function f(x) = -x3+3x-2 on the interval [-2,2] use derivative analysis to find: a.) The intervals on which f is increasing/decreasing. Label these clearly and explain your reasoning. b.) The absolute extrema of f. Label these clearly and explain your reasoning. c.) The intervals of concavity and any inflection points. Again, label these clearly and explain your reasoning. d.) Graph the function. Does it agree with the results of a-c? If not, discuss the differences.
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Given the function f(x) = -x3+3x-2 on the interval [-2,2] use derivative analysis to find:
a.) The intervals on which f is increasing/decreasing. Label these clearly and explain your reasoning.
b.) The absolute extrema of f. Label these clearly and explain your reasoning.
c.) The intervals of concavity and any inflection points. Again, label these clearly and explain your reasoning.
d.) Graph the function. Does it agree with the results of a-c? If not, discuss the differences.
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