A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
For the following function, find all its critical point(s) and its absolute extrema.
f(x)=10sqrt(x^2+10)−3x , 0<=x<=14
PLEASE HELP ! I need all the steps because I have no idea how to do this! Thanksss
anonymous
 5 years ago
For the following function, find all its critical point(s) and its absolute extrema. f(x)=10sqrt(x^2+10)−3x , 0<=x<=14 PLEASE HELP ! I need all the steps because I have no idea how to do this! Thanksss

This Question is Closed

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.01. calculate the derivative of f 2. find the roots of the derivative 3. check if those are local maxima, minima or saddle points, you could use the second derivative for that 4. compare the function values at the local extrema to the border points

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can you show me the actual solving of the derivative part? chain rule?

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0yes, just the basic rules, of course chain rule for the square root part, just try it on paper

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh my goodness, I typed the solution for you earlier, did you see it? I cant see it here now

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0f'(x) = [50x/[sqrt(x^2+10)]  3 = [10x  3sqrt(x^2+10)]/[sqrt(x^2+10)] By the definition of a critical number, the critical numbers can be obtained by solving 10x  3sqrt(x^2+10) = 0 and sqrt(x^2+10) = 0 From the first equation we get x^2 = 90/91. So x = sqrt(90/91) because x is between 0 and 14. From the second equation, note that there is no solution, so no critical number comes from here. So the critical point is (x,f(x)). This critical point will give a local extremum or an inflection point. But to find the absolute extrema, we don't have to know whether (x,f(x)) is a local extremum or not, you just need to compare the values of f(0), f(14) and f(sqrt(90/91)) and choose the largest and smallest value.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0nadeem you are right , thanks
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.