The graph of $g ( t ) = t ^ { 4 } + 2 t ^ { 3 }$ is concave up everywhere.

Name: The graph of $g ( t ) = t ^ { 4 } + 2 t ^ { 3 }$ is concave up everywhere.
Brand: Quizplus
Rating: 4.9 (37 reviews)

Question

Quizplus · Accepted Answer

The concavity of a function is determined by the sign of its second derivative. For $g(t) = t^4 + 2t^3$, the second derivative is $g''(t) = 12t^2 + 12t$. Setting $g''(t) = 0$ gives $t(t + 1) = 0$, which has solutions $t = 0$ and $t = -1$. This means the concavity can change at these points, so the graph is not concave up everywhere.

The Graph Of g(t)=t4+2t3g ( t ) = t ^ { 4 } + 2 t ^ { 3 }g(t)=t4+2t3

The Graph Of $g ( t ) = t ^ { 4 } + 2 t ^ { 3 }$