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3-130.

Summarize your understanding of first and second derivatives. Include information regarding increasing, decreasing, concavity.

When a function $f(x)$ is increasing and concave up: $f^\prime(x)> 0$ and $f^{\prime\prime}(x) > 0$.
When a function $f(x)$ is increasing and concave down: $f^\prime(x)$ _________ $0$ and $f^{\prime\prime}(x)$ __________ $0$.
When a function $f(x)$ is decreasing and concave up: $f^\prime(x)$_________ $0$ and $f^{\prime\prime}(x)$ __________ $0$.
When a function $f(x)$ is decreasing and concave down: $f^\prime(x)$ _________ $0$ and $f^{\prime\prime}(x)$ __________ $0$.