Find the Critical Numbers?

Question

1.) f(x) = 2x^3 + 3x^2 + 36x
x=?
2.) g(t) = |5t − 4|
t=?

Answer 1

No ideas at all?

Critical numbers are min, max, point of inflection, roots

min and max occur where f' = 0
inflection is where f'' = 0 and f' ≠ zero

The absolute value problem is tricky, since you can't rely on f' to get the min/max.

Observe, however, that |5t-4| is always at least zero.

It is zero only where 5t-4 = 0.