Find the followi points for f(x)=x^5+3x^3-10x^2+x+3

Question

zeros(x-intercepts)

local maximum

global maximum

local minimum

global minumum

Answer 1

The approach you need to follow is as follows:

1. Use the rational roots theorem to try to find the first of five roots [f(x)=0 for a certain x1]

2. Divide f(x) by (x-x1) using synthetic or long division

3. Repeat steps 1-2 twice on the 4th and 3rd order polynomial achieved this way as you find two more roots

4. Use the rational roots approach or quadratic formula (or tic-tac-toe etc.) to find the remaining two roots

5. Differentiate f(x) with respect to x and find zeroes for f'(x) using the same approach as outlined above. This will give you the 4 x values for all local maxima/minima

6. Find f''(x) or graph and/or use the (x+-deltax) approach to determine whether the extreme point is a max or min or just an inflection point

7. Calculate f(x=x1, x2, x3, x4), where x1-x4 are the 4 roots of f'(x) to determine which extreme points are local and which are global

 

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Good luck!

Alex