Posted by Sam on Thursday, March 17, 2011 at 2:41am.
The function f(x)=(x^4)(10x^3)+(18x^2)8 is continuous on the closed interval (1,8). Find the absolute minimum and maximum values for the function on this interval. Please help me!!! And please show your work so that i understand!! Thank you!!

Calculus  Reiny, Thursday, March 17, 2011 at 9:36am
find the derivative
dy/dx = 4x^3  30x^2 + 36x
set that equal to zero
4x^3  30x^2 + 36x= 0
2x(2x^2  15x + 18) = 0
2x(x6)(2x3) = 0
x = 0 or x = 6 or x = 3/2 , but x=0 lies outside our interval
so f(6) = ....
f(3/2) = ...
and for the endvalues
f(1) = ...
f(8) = ...
you do the arithmetic, and decide which is the highest and lowest f(x) value.
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