0
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ Slope of tangent at $x$ is equal to $f'(x)$. So calculate first derivative of function and create table of values $x$ and corresponding $f'(x)$. $\endgroup$ – mcihak Jul 11 '14 at 0:31
  • $\begingroup$ i know that its the derivative, but what values should I put? $\endgroup$ – Assab Amad Jul 11 '14 at 0:33
  • $\begingroup$ 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. $\endgroup$ – symplectomorphic Jul 11 '14 at 0:35
  • $\begingroup$ 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. $\endgroup$ – mcihak Jul 11 '14 at 0:36
  • $\begingroup$ 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? $\endgroup$ – Assab Amad Jul 11 '14 at 0:36
0
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.