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Given the graph of f' find the intervals the graph is increasing
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Learn how to sketch the graphs of f, f', f'', given any one of its graph. Given a function y = f(x), the derivative of the function y' = f'(x) represents the change in the value of the function with respect to a change in x. f'(x) indicates the slope of points on the curve describing the function. The second derivative of the function, y'' = f''(x) is the differentiation of the function twice. It indicates the concavity of the function and also the slope of the firsst derivative. Knowledge of this information helps in the sketching the f, f', and f'' of a function given the graph of one of them.
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