# Calculus - Rate of Change

Using the graph of the function $ƒ(x) = x^3 - x + 1$.

i. Find approximate x values for any local maximum or local minimum points.

ii. Set up a table showing intervals of increase or decrease and the slope of the tangent on those intervals.

iii. Set up a table of values showing "x" and its corresponding “slope of tangent” for at least 7 points

iv. Sketch the graph of the derivative using the table of values from (iii)

I am done up to ii, now how would I do (iii)? Do i just enter the values that make the slope of tangent zero and that would be only one value. What else can I put.

• Slope of tangent at $x$ is equal to $f'(x)$. So calculate first derivative of function and create table of values $x$ and corresponding $f'(x)$. – mcihak Jul 11 '14 at 0:31
• i know that its the derivative, but what values should I put? – Assab Amad Jul 11 '14 at 0:33
• Do exactly what it says. Make a table. Choose 7 arbitrary values of $x$. Find the slope of the tangent line at those seven points. – symplectomorphic Jul 11 '14 at 0:35
• It depends on you, you can choose arbitrary values. However better is not to choose values such as 1 000 000 000, because you have to sketch graf using these values. – mcihak Jul 11 '14 at 0:36
• so any random x-values and plug them into the derivative equation which is $3x^2-1$ and then find the f'(x) from those values? – Assab Amad Jul 11 '14 at 0:36

You can use whatever $c$ values you want, then show the corresponding values for the slope. The places the slope is $0$ would be reasonable to include, so you need at least five more. You are finding points on the graph of $f'(x)$, which you will graph in the next part.