Question : how can you find the steepest part of a curve?

Hi

How do you find the steepest part of a curve. I saw something on the internet that says you use second derivative = 0 to find points of inflection but

1) a second derivative = 0 doesn't guarantee a point of inflection does it?
2) even if it did, why is a point of inflection the steepest part of a curve

thanks

Answer : how can you find the steepest part of a curve?

Try this:

                       
         
           
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