Determine the y-intercept of the graph.
1 answer:
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One way to do it is with calculus. The distance between any point 
on the line to the origin is given by
Now, both
and 
attain their respective extrema at the same critical points, so we can work with the latter and apply the derivative test to that.
Solving for
, you find a critical point of 
.
Next, check the concavity of the squared distance to verify that a minimum occurs at this value. If the second derivative is positive, then the critical point is the site of a minimum.
You have
so indeed, a minimum occurs at.
The minimum distance is then
Now, both
Solving for
Next, check the concavity of the squared distance to verify that a minimum occurs at this value. If the second derivative is positive, then the critical point is the site of a minimum.
You have
so indeed, a minimum occurs at
The minimum distance is then
Answer:
f(x) = √(5-x)
Step-by-step explanation:
The square root is only defined for non-negative arguments. Here, we give it an argument that is only non-negative for x ≤ 5, thus satisfying the requirement for your function. The attached shows a table of values and a graph of it.
