The maximum value needs to be twice as great as what?
#How do I do this?
paper yew
lilac grail
The antiderivative function needs to be twice as great as the maximum value of the original function
paper yew
The antiderivative function needs to be twice as great as the maximum value of t...
I am still not understanding you.
The maximum value of the original function is 1, but the antiderivative is a whole function. You can't say that a function is twice as great as a number if it is not just a constant itself.
Is the statement of your exercise translated? If so, can you share the original?
lilac grail
Yeah right here
paper yew
Ah, there we go! That's more clear.
There is a problem, though. Arctangent doesn't have a maximum value, it only approaches it.
lilac grail
Ohhh that's probably why
paper yew
Well, let's say they meant supremum instead of maximum value.
arctan(x) tends to its supremum π/2 as x -> +∞.
So, arctan(x) + C -> π/2 + C, x -> +∞.
You need that to be twice the maximum value of the derivative, which is 1. So:
π/2 + C = 2
Solve it to get C, the graph it.
lilac grail
So C = 2-π/2