quintic means degree of 5.
a negative quintic would be: f(x) = -x⁵ <u>+ </u>
an example with one real zero could be: -x⁵ + x³ + x + 3 (see attachment)
Well let's start with y = -x^5 and y = - x^5 +1
The graph looks like the one on the right for these two. The red one is y = - x^5 and the blue one is y = - x^5 + 1
See below on the right
You can tell that these two are correct because there is only 1 x axis intercept for each of them. That means there is only 1 real solution which is what you are calling for.
Another one could be something like
y = -(x - 5)(x^2 + 2)(x^2 + 3)
The graph of that is on the left.
Given:
The height of a golf ball is represented by the equation:
To find:
The maximum height of of Anna's golf ball.
Solution:
We have,
Differentiate with respect to x.
For critical values, .
Differentiate y' with respect to x.
Since double derivative is negative, the function is maximum at .
Substitute in the given equation to get the maximum height.
Therefore, the maximum height of of Anna's golf ball is 6.25 units.