## Calculus: Early Transcendentals 8th Edition

$x=0$
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 $t=0$.