It is most likely a point of inflection for the graph. Q4) To find the maximum and minimum, do we find the 1st derivative or the 2nd derivative? You use the first derivative to find points where minimum and maximum occurs.The second derivative can help you tell which it is as explained in last part.Q5) What is the difference between relative maximum / relative minimum VS.......
FOR FIRST DERIVATIVES, the x values are the values where the function reaches critical points
which are possible extrema.
If f'(x) =0 then x is a critical point. At a zero value if the second derivative is >0 a
minimum for f(x) occurs at that x value
if the second derivative<0 then a maximum occurs
If the second derivative equals zero, then we need to examine the graph further to determine
what occurs. It is most likely a point of inflection for the graph.
Q4) To find the maximum and minimum, do we find the 1st derivative or the 2nd derivative?
You use the first derivative to find points where minimum and maximum occurs.
The second derivative can help you tell which it is as explained in last part.
Q5) What is the difference between relative maximum / relative minimum VS. relative extrema?
Relative Extrema are relative minimums and relative maximums. Relative Extrema which are biggest values in a range are called relative maximums while relative extrema that
are the smallest value in a range are called relative minimums.
Q1) The instantaneous rate of change of a function. How a function is changing at a certain point.
Q2) The same thing as Q1 but the instantaneous rate of change of the derivative of the function. How it is changing.
Q3) Ok if we have y=x^2 then dy/dx=2x. If you plug in a value for x, that tells you the slope of the tangent line at that x value of the original function.
Q4) Min/Max occurs when the graph changes from decreasing to increasing or increasing to decreasing respectively. So what you do is set the first derivative = 0 and see for what values of x for the original function of x has a 0 slope tangent line. Then you do a sign check with a value lower than that value of in your first derivative. If it is negative on the left and positive on the right, that means the function changed from decreasing to increasing and so it is a min. If it is positive on the right and negative on the left that means it is a max. Think of it like a hill. If a hill is sloping down and suddenly slopes up, then that point where it starts to slope up is a min.
Q5) Don't remember.
