Calculus
posted by Catherine .
Find the global maximum and minimum values of f(t)=4t/(2+t^2) if its domain is all real numbers?

f' = [4(t^2+2) 4t (2t)]/(t^2+2)^2
= [4t^2+8]/(t^2+2)^2
0 at max or min
t = + or  sqrt 2
f" = [ (t^2+2)^2 (8t) + 4(t^22)(2)(t^2+2)(2t) ] / (t^2+2)^4
if t = +sqrt 2
t^2+2 = 4
t^22 = 0
f" = [ 32 sqrt 2 +4*0 etc } /4^4
which is positive so a minimum
if t =  sqrt 2
t^2+2 is still 4
t^22 is still zero
so
f" = { +32 sqrt 2 .... etc
which is negative so a maximum
Respond to this Question
Similar Questions

Calculus
Use analytical methods to find the exact global maximum and minimum values of the function f(x)=8xln(4x) for x >0. If a global maximum or minimum does not exist, enter the word NONE. For the global maximum at x=none, But for the … 
calculus
Find the points at which y = f(x) = 5x−ln(5x) has a global maximum, a global minimum, and a local, nonglobal maximum on the interval .1 ≤ x ≤ 2. Round your answers to two decimal places. Global Minimum: (x,y) = (,) … 
calculus
Find the points at which y = f(x) = x8−13x has a global maximum and minimum on the interval 0 ≤ x ≤ 3.7. Round your answers to two decimal places. Global Maximum: (x,y) = (,) Global Minimum: (x,y) = (,) 
Algebra 2
3. Identify the vertex and the axis of symmetry of the graph of the function y = 3(x + 2)2 – 3. (1 point) A vertex: (2, –3); axis of symmetry: x = 2 B vertex: (–2, –3); axis of symmetry: x = –2 C vertex: (2, 3); axis of … 
URGENT ALGEBRA 2
identify the vertex and the axis of symmetry of the graph for the function y=3(x+2)^2 a.vertex(2,3 axis of symmetry x=2 b.vertex(2,3) axis of symmetry x=2 c.vertex(2,3) axis of symmetry x=2 d.vertex(2,3) axis of symmetry x=2 … 
algebra can someone help my buddy ray out
identify the vertex and the axis of symmetry of the graph for the function y=3(x+2)^2 a.vertex(2,3 axis of symmetry x=2 b.vertex(2,3) axis of symmetry x=2 c.vertex(2,3) axis of symmetry x=2 d.vertex(2,3) axis of symmetry x=2 … 
Calculus
Find the points at which y = f(x) = x^116x has a global maximum and minimum on the interval 0 ¡ x ¡ 4 Round your answers to two decimal places. Global Maximum: (x,y) = (,) Global Minimum: (x,y) = (,) 
Calculus
Find the points at which y = f(x) = x^116x has a global maximum and minimum on the interval 0 ¢®A x ¢®A 4 Round your answers to two decimal places. Global Maximum: (x,y) = (,) Global Minimum: (x,y) = (,) 
PreCalculus
Which of the following statements best describes the domain of the functions sine and arcsin? 
Math
What is the domain and range fro the expentiral function f(x)=2x4^x1+3?