# Thread: local max/min and inflection point

1. ## local max/min and inflection point

The derivative of a function is f'(x)= (x-1)˛(x+3).
Find the value of x at each point where f has a
(a) local maximum
(b) local minimum
(c) point of inflection

I got that the maximum is at x=-3, and minimum at x=1. I got x=-5/3 and x=1 as points of inflection.
Can anyone tell me if I'm right, please?

2. Originally Posted by h4hv4hd4si4n
The derivative of a function is f'(x)= (x-1)˛(x+3).
Find the value of x at each point where f has a
(a) local maximum
(b) local minimum
(c) point of inflection

I got that the maximum is at x=-3, and minimum at x=1. I got x=-5/3 and x=1 as points of inflection.
Can anyone tell me if I'm right, please?
solve where derivative is zero and then check the signs on different intervals

3. The answers you have are for the graph of f'. You use f' to find where f is increasing and decreasing. If you put the graph of f' into your graphing calculator, you will see that it is negative (below the x axis) from - infinity to -3 and positive (above the x axis) from -3 to infinity. What this tells you is that the graph of f is decreasing (could be negative or positive) to the left of -3 and increasing (negative or positive) from -3 to 1 and also to the right of 1.

A minimum or maximum on the graph of f only occurs if there is a change from decreasing to increasing or vice versa. Since you only have one change of sign (which occurs when the derivative =0) this will be your local minimum. The graph of f does not have a local maximum. Now, f' does = 0 at x=1, but notice in the equation of f' that this zero has a power of 2. This tells you that it does equal zero at 1, but it only touches the x-axis, it does not cross it. So, there is no sign change at x=1 and therefore is not a candidate for max or min.