A few days ago

How can you sketch the graph of the original function if only given the graph of the first derivate?

Calculus question…

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A few days ago

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The first derivative is the slope so if it’s below the x-axis, the slope is negative so the graph is falling from left to right; if it’s on the x-axis the slope is zero so there is a critical point, and if above, slope is rising so it’s going up from left to right. You can never get the correct position (up or down) from just the first derivative; for example if f ‘(x) is 2x, f(x) could have been x^2 or x^2 + 10 or +/- any other number for that matter but you can get its shape.