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Find the largest value of A such that the functiont^3+5t^2-5t+7is decreasing for all t in the interval (0,A)?
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- 1 decade agoFavorite Answer
A function is decreasing when the derivative of the function is negative.
f'(t)=3t^2+10t-5
Find the zeroes of the derivative by using the quadratic formula, and you should get:
t=(-10+/-sqrt(160))/6=(-5+/-2sqrt(10))/3
You can plug in values to see that f'(0) is negative up to (-5+2sqrt(10))/3, at which point it becomes zero and to the right of that it is positive. So, A= (-5+2sqrt(10))/3
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