# Maxima and minima

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• Feb 28th 2007, 02:17 AM
arunkayal
Maxima and minima
Hi All,
Please help me to solve this:

For the following function, find a point of maxima and a point of minima, if these exist:

f(x) = 17x5 – 14x3 + 44.

Thanks
Arun
• Feb 28th 2007, 06:37 AM
Soltras
Quote:

Originally Posted by arunkayal
Hi All,
Please help me to solve this:

For the following function, find a point of maxima and a point of minima, if these exist:

f(x) = 17x5 – 14x3 + 44.

Thanks
Arun

Well, for starters take the first derivative so you can see where the polynomial's critical points are.

\$\displaystyle f'(x) = 85x^4 - 42x^2\$

The roots of this function are the extrema of the original function. That is, set \$\displaystyle 0 = f'(x)\$ and solve (hint recognize that 0 must be a root, so to find others, solve \$\displaystyle f'(x)=85x^2-42\$.)

Take the next derivative and substitute in the critical points found above. If the result is negative then it's a max. If it's positive then it's a min. If it equals zero, then the point is neither max or min (throw it out), unless the whole original function is constant, which it is not in this case.
• Mar 3rd 2007, 11:45 PM
qbkr21
Re:
This problem can be summed up easily by following these four steps:

1. Write the function
2. Compute its derivative
3. Set the derivative equal to zero and solve for x
4. Take x coordinate(s) and insert back into the original function

These steps are also known by Math Professors as finding the Critical Points.

Best of Luck!