Posted by casey on Thursday, November 5, 2009 at 4:32pm.
let f(x)= x^2 +3x on the interval [1,3] . Find the absolute maximum and absolute minimum of f(x) on this interval

calc  MathMate, Thursday, November 5, 2009 at 6:02pm
The absolute maximum and absolute minimum of implicit equations are difficult to find because of the uncertainty of the number of local maxima and minima.
For a quadratic equation, we know that there is only one single maximum/minimum which will automatically be the global value. If a global maximum falls within the interval, the smaller value of each of the limits will give the minimum within the interval.
Thus, interval = [1,3].
f(x)= x^2 +3x
f'(x)=2x+3
f'(x)=0 at x=1.5, falls within [1,3]
f"(x)=2 f'(1.5) is a maximum.
Thus the maximum is at x=1.5, or f(1.5)=2.25.
The minimum is one of the two following values (evaluated at the limits of the given interval).
f(1) or f(3).
Can you take it from here?
Answer This Question
Related Questions
 Calculus (pleas help!!!)  Find the absolute maximum and absolute minimum ...
 Calculus (pleas help!!!)  Find the absolute maximum and absolute minimum values...
 Calculus  Find the absolute maximum and absolute minimum values of the function...
 calculus  2) Let g(s)= t(4−t)^1/2 on the interval [0,2]. Find the ...
 calc  Let g(s)=1/(s2)on the interval (0,1). Find the absolute maximum and ...
 Calculus  Let f(t)=t\sqrt{4t} on the interval [1,3]. Find the absolute ...
 calculus  Let g(x)=(4x)/(x^2+1) on the interval [4,0]. Find the absolute ...
 calculus  Let g(s)=1/(s2) on the interval [0,1]. Find the absolute maximum and...
 calculus  Let f(x)=x^2+3x on the interval [1,3]. Find the absolute maximum and...
 Calculus  Find the absolute extrema of the function on the interval [2, 9]. (...
More Related Questions