This is the first derivative from a quartic, I'm just trying to find the min and max

0.36x^3 - 0.84x^2 +5.52x - 6.84 = 0

I thought about making them all fractions? Like:

9x^3/25 - 21x^2/25 +138x/25 - 171/25 = 0

but I wasn't sure how to work it out from there

Yes, that was a good idea, then multiply every thing by 25 to get rid of the denominators, and you are left with:

9x^3 - 21x^2 + 138x - 171 = 0

But you can still divide everything by 3 to get

3x^3 - 7x^2 + 46x - 57 = 0

From here, the easiest thing to do is using polynomial root calculation program (available online) to get

ONE REAL ROOT: x = 1.356

Then take the SECOND derivative to see if it's curving up or down. (+) is min, (-) is max

Then plug into the original equation to get the y coordinate of the point.

Thank you Vincent, that was a tremendous help. Would you be able to help me with one more?

I have to find the min and max of the first derivative of an Exponential equation. The first derive is:

y`= 1.19 * 1.07^x

for that one there is NO value of x that would make y' = 0. The closest would be x = - infinity, but that's undefined.

Ah ok.

Would that in turn mean there are no inflection points for the second derivative of:

y =0.81 * 1.07^x

because of the same reasoning?

Not necessarily. There can be no relative maximums or minimums and still have an inflection pt.

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