Determine a,b,c and d so that the graph of
has a point of inflection at the origin and a relative maximum at the point (2,4)
so
and
For a point of inflection,
So at (origin)
.
Now at (2,4) as we have a local maximum, and we must make sure so it is a max and not a min.
Substituting in the values:
(b is gone as it equals zero)
Now, we know that
We know that at , , so you can see .
Now we get .
You know that at , . Simply substitute these values into the equation to find a. Then you can find c.
Hello, Rimas!
Since the origin (0,0) is on the graph: .Determine so that the graph of: .
has a point of inflection at the origin and a relative maximum at the point (2, 4)
. . We have: .
The function is: .
The first derivative is: .
The second derivative is: .
Since the origin is an inflection point: .
. . We have: .
The function is: .
Since (2, 4) is on the graph: .
. . .[1]
Since (2, 4) is a critical point: .
. . We have: . .[2]
Equate [1] and [2]: .
Substitute into [2]: .
Therefore: .