All you need is that
Now we have
Setting equal to zero and factoring gives
This will give you both the max and min values.
Algebraically determine the maximum value of the y-coordinate of points on the cardioid for 0 ≤ θ ≤ π.
I used the formula:
, which yielded .
If I solve , setting it to zero, it will give the value of theta at which horizontal tangents exist. The problem is that I don't know how to solve it.
After graphing it, I know that the max value occurs when and , but I'm not sure how to get to those values.
Hello, Algebrah!
Determine the maximum value of the y-coordinate of points on the cardioid:
We have: .Code:| | * * * |* * *| * * | | * * | * | * | * - - - * - - - - - - - * - - - |
We have: .
. . . .
. . . . .
. . . . . . . . . .
n . . . . . .
. .
** There is a horizontal tangent at
. . .but it gives a minimum value for y.
Hence, the maximum y occurs at