# Thread: Using the graph of the Function

1. ## Using the graph of the Function

$\displaystyle f(x) = x3 - x + 1$
a) Find approximate x values for max/min points.
b) Set up a table showing intervals of increase or decrease and the slope of the tangent on those intervals.
c) Set up a table of values showing "x" and its corresponding “slope of tangent” for at least 7 points
d) Sketch the graph of the derivative using the table of values from (c)

2. What have you done so far?

For a) you should just plot some points. For example choose x to be -3,-2,-1,0,1,2,3 and then if you need to you can plot more points in between to get a nice curve. Then using the graph, you can find approximately where the min/max occur.

For b) You can use the plot you just made. Intervals of increase are intervals where if x is increasing so is f(x). It's the opposite for intervals of decrease. The slope of the tangent, you can either use the derivative to calculate it, or you can just use the approximation rise/run from the points you plotted.

For c) i think you need to actually calculate it.

For d) you do need the data from c)

3. i found the derivative and using that i was trying to find max/min

4. Originally Posted by ilovemymath
i found the derivative and using that i was trying to find max/min
Setting this to zero and solving will get you the exact values for min/max not the approximate values.

5. so i'll have to do the way vlasev suggested?