I need your help with this question:

The tangent line to the function f(x) at x=1 is y=3x-2. Find f(x) (without using integrals).

I know that the derivative at x=1 should be 3, but without more information, how am I suppose to find f(x) ? This is a multiple answers question, but at least 3 answers gives a derivative of 3 when putting x=1.

Thank you.

  • $\begingroup$ You need $f'(1)=3$, but also $f(1)=1$. $\endgroup$ – Yves Daoust Jun 17 '16 at 13:05
  • $\begingroup$ Obviously many functions satisfy $f(1)=1),f'(1)=3$. What are the alternatives given? $\endgroup$ – almagest Jun 17 '16 at 13:06
  • $\begingroup$ The question seems poorly written; the correct answer should be "there is no way to know." If indeed they want you to pick the function that satisfies $f(1)=1$ and $f'(1)=3$, then they should have written, "Which of the following functions could be a candidate for $f(x)$?" $\endgroup$ – Théophile Jun 17 '16 at 13:09
  • $\begingroup$ I agree with you ! $\endgroup$ – user3275222 Jun 17 '16 at 13:13

You can't find $f(x)$ because you aren't given enough information. There are many functions that share the same tangent line at a given point.

But you can find $f(1)$ because $f(1)=\ell(1)$, where $\ell$ is the function whose graph is the given tangent line (i.e., $\ell(x)=3x-2$). That's because the tangent at $x=1$ passes through the point $(1,f(1))$.

EDIT: Sorry, I didn't see that you actually do have more information that you aren't telling us.

Note that you really have both $f'(1)=\ell'(1)=3$ and $f(1)=\ell(1)=1$. You may be able to eliminate all but one of the possible answers with this.

Can you also please give us the actual answers you have to choose from?

| cite | improve this answer | |
  • 1
    $\begingroup$ But he has enough info. It is a multiple choice question. He just hasn't given it to us yet, so this is premature! $\endgroup$ – almagest Jun 17 '16 at 13:07
  • $\begingroup$ @almagest: Ah, you are right. I didn't read the entire question. My bad. I edited my answer. $\endgroup$ – MPW Jun 17 '16 at 13:08
  • $\begingroup$ Can e^(3*(x-1)) be the correct answer? $\endgroup$ – user3275222 Jun 17 '16 at 13:11
  • $\begingroup$ @user3275222: If $f(x)=e^{3(x-1)}$, then $f(1)=e^0=1$, and $f'(1)=3e^0=3$. So yes, that is a possible candidate. $\endgroup$ – MPW Jun 17 '16 at 13:13
  • $\begingroup$ Thanks, problem solved (and sorry for not writing the expression properly, not controlling latex yet). $\endgroup$ – user3275222 Jun 17 '16 at 13:17

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.