Question 1096536
{{{ P(t) = t^3 - 18t^2 + 81t }}}
{{{ P(0) = 0 }}}
{{{ P(3) = 3^3 - 18*3^2 + 81*3 }}}
{{{ P(3) = 9 - 162 + 243 }}}
{{{ P(3) = 90 }}}
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{{{ P(5) = 5^3v - 18^5^2 + 81^5 }}}
{{{ P(10) = 10^3 - 18*10^2 + 81*10 }}}
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Here's the graph:
{{{ graph( 400,400, -20,20,-30,200, x^3 - 18x^2 + 81x ) }}}
The derivative ( is this a calculus problem? ) tells you when
the function is increasing or decreasing
{{{ graph( 400,400, -20,20,-30,200, x^3 - 18x^2 + 81x, 3x^2 - 36x + 81 ) }}}
The funtion {{{ P(t) }}} is decreasing between the roots of the quadratic.
( find the roots usinf quadratic fromula )