How do you find the intervals on which the graph

veleumnihryz

veleumnihryz

Answered question

2022-04-23

How do you find the intervals on which the graph of f(x)=5x1 is concave up or is concave down, and find the x - coordinates o the points of inflection?

Answer & Explanation

Volsa280

Volsa280

Beginner2022-04-24Added 16 answers

Step 1
Unless required, I would not use calculus for this.
The graph of the square root function is:
In f(x)=5x1, the 5 stretches the graph vertically and the -1 translates down 1.
It is clear that the graph is concave down on (0, )
Since the concavity does not change, there are no inflection points.
If I am required to use calculus:
Note that the domain of f is
f(x)=52x
f(x)=54x3 is always negative on (0, )
Therefore, the graph of f is concave down.

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