# Single variable calculus question. (first post)

physicsstudent04
Hi I'm new to this forum.
I was wondering if anyone can explain to me how to do a first derivative test to find the relative extrema. I've been trying to read it, but it just isn't sinking in. thanks in advanced.

NateTG
Homework Helper
If a function is continuous and differentiable then local maximums amd minimums occur where the graph of a function is flat, so they occur where the derivative is zero.

So, when looking for maximums and minimums you only need to check endpoints, and points where the derivative is zero or doesn't exist.

mathman
There is third possibility for zero derivative points, horizontal inflection point. Example y=x3, at x=0.

physicsstudent04
thanks a lot guys. appreciate the help.

reinhard_t
please open the attachment below, to get better picture...
(note : that the picture is the graph f(x) against x )

actually to see the better idea of first derivative by imagining it as a gradient of the graph of a fuction.

suppose I have fuction f(x)

when you derive it becomes f'(x)...
what is f'(x) ???

now look at the picture that there are 3 red straight lines.you can get line straight ,if and only if at the turning point like what you see in the graph

at the other point you will find the line is slope like both the blue line.

remember that straight line has gradient 0....that is to say, f'(x)=0

so to find either maxima or minima ,you must find value of x ,which can be subtituted into f'(x) and get value 0.

#### Attachments

• derivative.jpg
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