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11 Jun 2020

Graphical Reasoning

Consider the function

.

(a) Determine the changes (if any) in the intercepts, extrema, and concavity of the graph of f when a is varied.

(b) In the same viewing window, use a graphing utility to graph the function for four different values of a.

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Rico Jay Laxa
Rico Jay LaxaLv10
25 Jun 2020

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Related questions

Graphical Reasoning

Consider the function f(x) = tan(sin x).

(a) Use a graphing utility to graph the function.

(b) Identify any symmetry of the graph.

(c) Is the function periodic? If so, what is the period?

(d) Identify any extrema on (–1, 1).

(e) Use a graphing utility to determine the concavity of the graph on (0, 1).

Graphical Analysis Consider the functions f and g, where

and

(a) Use a graphing utility to graph f and g in the same viewing window.

(b) Explain why g is nonnegative.

(c) Identify the points on the graph of g that correspond to the extrema of f.

(d) Does each of the zeros of f correspond to an extremum of g? Explain.

(e) Consider the function

Use a graphing utility to graph h. What is the relationship between g and h? Verify your conjecture.

Graphical Reasoning Consider the function .

(a) Use a graphing utility to graph the function and estimate the values of . and f'(2).

(b) Use your results from part (a) to determine the values of , and .

(c) Sketch a possible graph of .

(d) Use the definition of derivative to find

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