If f(x) is concave down, then f”(x) is?
If f(x) is concave down, then f”(x) is negative or less than zero
If f(x) is concave down, then f”(x) is negative or less than zero.
To understand this, let’s first define what it means for a function to be concave down. A function is said to be concave down if its graph curves downward, resembling an upside-down U shape.
The second derivative of a function, denoted as f”(x), represents the rate of change of the slope of the function with respect to x. In simpler terms, it tells us how the slope of the function is changing at each point.
When the second derivative of a function is negative or less than zero (f”(x) < 0), it means that the slope of the function is decreasing as we move along the x-axis. Consequently, the graph of the function will curve downward, indicating that the function is concave down. Therefore, if f(x) is concave down, then f''(x) is negative or less than zero.
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