Question

Can someone tell me how to do this problem?

Answer 1

C-intercept(s): (0,0)

t-intercept(s): (0,0), (6,0), (-4,0)

Explanation:

the C-intercept is essentially the y intercept. this occurs when t=0:

C(0) = 4(0)^4 - 8(0)^3 - 96(0)^2 = 0. so the C-intercept is at (0,0).

the t-intercept is the x-intercept, and occurs when C(t) = 0:

4t^4 - 8t^3 - 96t^2 = 0 =
`4t^(2) (t-6)(t+4)`. C(t) = 0 when t = 0, t= 6, and t = -4.