Question

Calculus Help!

Answer 1

I attempted to find the local minima and maxima of the equation (3/1000)x^3-(7/100)x^2+(8/10)x. I found the derivative to be (9/1000)x^2-(14/100)x+(8/10). I solved for zero for the locations of the places with no slope. It gave me a complex root. Why is this?

Answer 2

because the original function has no local min or max.

Answer 3

I see that it has a saddle point, but I thought it still had a real solution for where the point of no slope would be. If the equation yielded zero substituting the solutions of the derivative, then I thought it would be a saddle point.

Answer 4

I'm not sure about that. I think there's an inflection point

Answer 5

but it doesn't appear to be a point where slope is 0

Answer 6

Don't all inflection points have slope 0?

Answer 7

not necessarily. Consider
\(f(x) = x^3 + 5x²^2\)
\(f'(x) = 3x^2 + 10x\)
\(f''(x) = 6x + 10\)

There's an inflection point at x = -5/3, but the slope there is -25/3

Answer 8

Thanks for the help, I see what you mean.

Answer 9

you're welcome