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Numerade Educator

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Problem 64 Hard Difficulty

If $ \displaystyle f(x) = \int^x_0 (1 - t^2) e^{t^2} \,dt $, on what interval is $ f $ increasing?

Answer

increasing when $|x|<1,$ decreasing otherwise

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Video Transcript

Okay, The first thing you know is the directive one minus X squared times E to the X squared. Now we know that we have one month's ex, Corde said. Equal to zero axes, Juan or negative one cause one are negative on squared, sort of this positive one know either the export always has to be positive. Therefore, we know that when access between negative 11 the function is increasing, so it's increasing. The absolute value of axe is less than one. That's essentially this simplified form in which we can write this, otherwise it's decreasing.