Calculus
posted by John on .
Find the Critical Numbers?
1.) f(x) = 2x^3 + 3x^2 + 36x
x=?
2.) g(t) = 5t − 4
t=?

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 5t4 is always at least zero.
It is zero only where 5t4 = 0.