Concept explainers
To Draw:
Graph of the function
Solution:
The graph is drawn below.
Given:
Explanation:
Consider, the function
(1) Domain of the function y:
Domain of
Domain of
(2) Intercepts:
For y-intercept, put x = 0 in the function y:
Therefore, (0,1) is y-intercept. Since range of exponential function is
(3)
This implies that y is neither even nor odd function.
(4) Asymptotes:
Since the function y is finite for all values, therefore, it has no vertical asymptote.
Horizontal asymptotes:
Consider
Thus, y =0 is horizontal asymptotes.
(5) Increasing or decreasing:
Consider
Differentiate it with respect to x, we get
Put
Consider
Interval | Point in the interval | Value of |
Sign of |
Increasing or decreasing |
Increasing | ||||
Decreasing |
This implies that
(6) Local maxima or minima:
Consider
Differentiate it with respect to x, we get
At
Therefore,
(7) Inflection point:
Put
Now,
And
Therefore, in the intervals
Thus, by the above information’s graph of y is:
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Check out a sample textbook solutionChapter 6 Solutions
Calculus (MindTap Course List)