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Let 

\[f(t) = \int_0^t (x - 7)(x - 4)(x + 1)(e^x - 1) \left( \arctan (x) - \frac{\pi}{3} \right) \: dx.\]

Find all values of t where f(t) has a local minimum at t

 

Sorry, I put this question again, but the answer was in decimals but i need it in simplifed.

 Jan 6, 2021
 #2
avatar+112031 
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Where is your original question ?

Please include a link to it.

 Jan 12, 2021
 #3
avatar+112031 
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Maxima and minima occur when the first derivative, (which is the gradient) is 0

 

So what is the first derivative of f(t)    ?      

 

Hint:  what is the opposite of integration?

 

Here is a graph that you might find useful.

https://www.desmos.com/calculator/ku32fssw2e

 Jan 14, 2021
edited by Melody  Jan 14, 2021

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