A bird is flying at height y that is a function of its distance from a tree x given by y = 3x^3 + 2x^2 - 10x + 5 . What is the maximum height of the bird.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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.

Last Updated by eNotes Editorial on
An illustration of the letter 'A' in a speech bubbles

The distance of the bird from its nest is the magnitude of a vector which is a non-negative number.

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial