Find the critical numbers of the function s(t)=3t^4+4t^3-6^2
To find the critical numbers of a function, we need to find the values of t where the derivative of the function is either zero or undefined.
First, let's find the derivative of s(t). The derivative of a polynomial function is obtained by differentiating each term with respect to t.
s'(t) = 12t^3 + 12t^2
Next, let's set the derivative equal to zero and solve for t to find the values where the derivative is zero.
12t^3 + 12t^2 = 0
Factoring out 12t^2:
12t^2(t + 1) = 0
Setting each factor equal to zero:
12t^2 = 0 -> t = 0
t + 1 = 0 -> t = -1
So the critical numbers of the function s(t) = 3t^4 + 4t^3 - 6t^2 are t = 0 and t = -1.