# Thread: Maxima and minima

1. ## Maxima and minima

Hi All,

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

f(x) = 17x5 – 14x3 + 44.

Thanks
Arun

2. Originally Posted by arunkayal
Hi All,

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.

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

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

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.

3. ## 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!