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calculus question about integrals/density?
im working on an assignment and one of the questions asks to find the minimum and maximum density of a snake that is 2m long and its density is described by the function d(x)=1.0+2.0*10^-8x^2"(240-x)
after finding the max/min it asks where the maximum occurs, which im also struggling with.
i know how to find the total mass as well as the average density, but i was wondering if anyone could explain how to do the first parts. thanks
i found the derivative to be
d'(x)=-6.0*10^-8x^2 + 9.6*10^-6x -1.0
but i dont think this is right because it doesnt work with the quadratic equation
to find the derivative i just used the product rule, is this right? does anyone know where i went wrong?
1 Answer
- 1 decade agoFavorite Answer
the maximum occurs at the highest and lowest points of the curve, which is where the curve changes direction. so the slope will equal zero at its highest and lowest points. take the derivative, set it equal to zero, and solve. then take those values and plug them into the original equation. those values will tell you where the max and min occur.
