Math  /  Calculus

QuestionUse derivatives to find the critical points and inflection points. f(x)=5x6lnxf(x)=5 x-6 \ln x
Enter the exact answers in increasing order. If there is only one critical point, enter NA in the second area. If there are no inflection points, enter NA.
Critical points: x=x=\begin{array}{l} x=\square \\ x=\square \end{array}
Inflection point: x=x= \square

Studdy Solution
Determine the inflection points by setting the second derivative equal to zero and checking for sign changes.
6x2=0 \frac{6}{x^2} = 0
This equation has no solutions because 6x2\frac{6}{x^2} is never zero for any real xx. Therefore, there are no inflection points.
The critical point is at x=65x = \frac{6}{5}.
Critical points: x=65x=NA \begin{array}{l} x=\frac{6}{5} \\ x=\text{NA} \end{array}
There are no inflection points.
Inflection point: x=NA x = \text{NA}

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord