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Numerade Educator



Problem 48 Easy Difficulty

If $ f(2) = 10 $ and $ f'(x) = x^2 f(x) $ for all x, find $ f''(2). $



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Video Transcript

it's clear. So name read here. So we're gonna use our product rule. Then we get us The drug builder of it is is equal to two x of X plus X squared times, the derivative of the We know that the derivative of off to is equal to two square time's up of two, which is equal to four times 10 which gives us 40. So when we plug it in to our equation here we get the second derivative of up of two is equal to two times two times 10 plus two square plus 40 which is equal to 200.