How Decreasing F'(X) Indicates Negative F”(X) For Graphs Of Functions – An Explanation For Math Enthusiasts.

If f'(x) is decreasing, then f”(x) is?

f'(a)

If f'(x) is decreasing, it means that the slope of the tangent line to the graph of f(x) is decreasing. This indicates that the rate of change of f(x) is decreasing, which implies that f”(x) is negative.

To understand this concept more intuitively, think of a curve that is initially steep (positive slope) and then gradually becomes less steep (decreasing slope). At the point where the curve is changing from being steep to less steep, its slope was decreasing. This corresponds to a negative acceleration, which is reflected in f”(x) being negative.

Therefore, we can conclude that if f'(x) is decreasing, then f”(x) is negative.

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