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Numerade Educator

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Problem 33 Medium Difficulty

Find the critical numbers of the function.

$ g(t) = t^4 + t^3 + t^2 + 1 $

Answer

$$g(t)=t^{4}+t^{3}+t^{2}+1 \Rightarrow g^{\prime}(t)=4 t^{3}+3 t^{2}+2 t=t\left(4 t^{2}+3 t+2\right)=0$$

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Video Transcript

OK, taking the derivative. We end up with four t cubed plus three t squared prostitute T We know that we can right this as t on the outside. Okay, Now we know that if we set this equal to zero, then we know that we have a singular solution which would be t equals zero. We don't get anything from this inside. So from what's in parentheses, we don't get anything from fact during this. But if we set what's on the outside T equals zero, we end up with t equals zero is the critical number.