Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Let f(x) be a function plotted on x y axis, then is the slope of the graph.
The graph of the function given in the question is given below(adding some points).
Consider the function from to . Here, the function value is increasing. Therefore the slope is positive. Thus, the graph of f'(x) will be positive.
Consider the function from to . Here, the function value is increasing. Therefore the slope is positive. Thus, the graph of f'(x) will be positive.
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