Answer
$x=0$
Work Step by Step
Original Equation:$g(t)= t^{4} +t^{3}+t^{2}+1$
Critical points of a function occur when the derivative is zero or the function is undefined. In this case, we have a polynomial, which means that the function is always defined. This means we need to see when the derivative is zero.
Finding the derivative through the power rule:
$g'(t)= 4t^{3} +3t^{2}+2t$
Setting the derivative to zero:
$4t^{3} +3t^{2}+2t = 0$
The t value which makes the above equation is $t=0$, therefore the critical point of this equation is when $t=0$.
