When f ‘(x) is increasing, f(x) is
concave up
When f ‘(x) is increasing, it means that the slope of the tangent line to the graph of f(x) is increasing as we move from left to right on the x-axis. This implies that the rate at which f(x) is changing is increasing as well. In other words, as we move from left to right on the x-axis, the curve of f(x) is getting steeper and steeper.
Therefore, we can conclude that when f ‘(x) is increasing, f(x) is also increasing at an increasing rate or getting steeper. In other words, the curve of f(x) is becoming more and more curved as we move from left to right on the x-axis.
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