anonymous
  • anonymous
For the following function, find all its critical point(s) and its absolute extrema. f(x)=10sqrt(x^2+10)−3x , 0<=x<=14
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
To find the critical point(s), we will look at the derivative of f and solve f'(x)=0: f'(x) = 10x/[sqrt(x^2+10)] - 3 = 0 Make the left hand side into a single fraction and for the fraction to be zero, its numerator must be zero. So 10x - 3sqrt(x^2+10)=0 10x = 3sqrt(x^2+10) 100x^2 = 9(x^2 + 10) x^2 = 90/91 x1 = sqrt(90/91) or x2 = -sqrt(90/91) The critical points are (x1,f(x1)) and (x2,f(x2)). To find the absolute extrema, you can either use Second Derivative Test or First Derivative Test. The second derivative of f is f"(x) = (x^3 -10x^2 +10x)/(x^2+10)^(3/2)
anonymous
  • anonymous
Some correction. Since x is between 0 and 14, only x1 above will be considered for the critical point. Besides that, since f'(x) is f'(x) = [10x - 3sqrt(x^2+10)] / sqrt(x^2+10), the critical point also can occur when the denominator, sqrt(x^2+10) of f' is 0. This comes from the definition of a critical number: a number c is a critical number of f if f'(c) = 0 or f'(c) does not exist. But sqrt(x^2+10) = 0 has no solution, so only x1 above is the critical number for f.

Looking for something else?

Not the answer you are looking for? Search for more explanations.