If f(x) is concave down, then f”(x) is?
f”(x) = negative
If a function f(x) is concave down, it means that it is curving downwards or has a decreasing rate of change. In other words, as we move from left to right along the function, the slope of the tangent lines to the function is also decreasing.
The second derivative of the function, denoted as f”(x), tells us about the curvature of the function. A positive second derivative indicates that the function is concave up, i.e., the slope of the tangent lines is increasing. On the other hand, a negative second derivative indicates that the function is concave down, and the slope of the tangent lines is decreasing.
Therefore, if f(x) is concave down, then f”(x) is negative. This is because the decreasing slope of the tangent lines indicates a negative curvature, which is reflected in the negative value of the second derivative.
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