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Applications of differentiation

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Slope and concavity are different

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Four source configurations with tangent segments: case 1 increasing concave down, tangents above on (a,b); case 2 increasing concave up, tangents below on (c,d); case 3 decreasing concave down, above on (c,d); case 4 decreasing concave up, below on (a,b). Each panel shows both derivative signs.
Four source configurations with tangent segments: case 1 increasing concave down, tangents above on (a,b); case 2 increasing concave up, tangents below on (c,d); case 3 decreasing concave down, above on (c,d); case 4 decreasing concave up, below on (a,b). Each panel shows both derivative signs.
Four source configurations with tangent segments: case 1 increasing concave down, tangents above on (a,b); case 2 increasing concave up, tangents below on (c,d); case 3 decreasing concave down, above on (c,d); case 4 decreasing concave up, below on (a,b). Each panel shows both derivative signs.
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