The height of the bird (y) is a function of its distance from its nest (x). The relation between the two is y = 3x^3 + 2x^2 - 10x + 5.
The height of the bird has a maximum value at the solution of y' = 0, x = a and if y''(a) is negative.
y' = 9x^2 + 4x - 10
y' = 0
=> 9x^2 + 4x - 10 = 0
=> `x = (-4 +- sqrt(16 + 360))/18`
=> `x = (-4 +- sqrt 376)/18`
=> `x = (-2 +- sqrt 94)/9`
y'' = 18x - 4
At `x = (-2 + sqrt 94)/9` , y'' is positive and at `x = (-2 - sqrt 94)/9` , y'' is negative. But the distance of the bird from its nest cannot be negative. As the second derivative of y is not negative for a valid value of x, there is no maximum limit to the height of the bird.
There is no maximum value to the height at which the bird flies.