Question

Find the critical numbers and absolute extrema for y = 2x³ - 39x² + 240x on the interval [4, 9].

Type DNE if an answer does not exist.

Answer 1

Critical Numbers: 5 and 8

Minimums is f(4)

Maximum is f(5)

Explanation:

Take the derivative of the function using the power rule to get

`6x^2-78x+240\\x^2-13x+40\\(x-5)(x-8)`

This gives you the critical numbers then you have to evaluate at all points:

`f(4) = 464 \\f(5) = 475\\f(8) = 448\\f(9) = 459`

Showing the minimum is f(4) and the maximum is f(5)