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.
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!