Question

Find the transition points.

y = 7x^3 + 168x^2

(Use symbolic notation and tions where needed. Give your answer in the form of a comma separated list)

Answer 1

The transition points of the function y = 7x^3 + 168x^2 are found by differentiating the function and setting the derivative to zero. The critical points occur at x = 0 and x = -16.

Step-by-step explanation:

To find the transition points of the function y = 7x^3 + 168x^2, we need to determine the points where the function changes from increasing to decreasing or vice versa. These occur at the critical points, which are found by taking the derivative of the function and setting it to zero.

The first step is to differentiate the function:

y' = 21x^2 + 336x

Then we set the derivative equal to zero to find the critical points:

0 = 21x^2 + 336x

Factoring out the common term x gives:

0 = x(21x + 336)

This equation is satisfied when x = 0 or x = -16. These are the transition points of the given function.

Therefore, the transition points are at x = 0 and x = -16.