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# Find the critical numbers of the function.$g(t) = t^4 + t^3 + t^2 + 1$

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

Derivatives

Differentiation

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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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.

#### Topics

Derivatives

Differentiation

Volume

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp