Calculus
posted by Salman .
Determine where the absolute extrema of f(x)=3(x^2)+7x on the interval [1,3] occur.
1. The absolute maximum occurs at =
2. The absolute minimum occurs at =

Set the derivative f'(x) = 0 and solve for x.
6x + 7 = 0
x = 7/6
Since the second derivative f"(x) = 6, the extremum at x = 7/6 is a maximum. The minimum for the interval [1,3] will occur at x = 3, since the f(x) just keeps getting lower for higher values of x when x > 7/6.
Respond to this Question
Similar Questions

Calculus (pleas help!!!)
Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter 1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum … 
Calculus (pleas help!!!)
Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter 1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum … 
Applied Calculus
Find the absolute extrema of the function on the interval [2,3]. (Round your answers to the nearest hundredth.) Absolute Minimum ___ at x=___ Absolute Maximum ___ at x=___ 
Calculus
Find the absolute extrema of the function on the interval [2, 9]. (Round your answers to the nearest hundredth.) g(x)=x/(ln(x)) Absolute minimum: at x = Absolute maximum: at x = 
Calculus
Find the absolute maximum and absolute minimum values of the function f(x)=x^3+6x^263x+4 on each of the indicated variables. Enter DNE for does not exist. (A) Interval = [8,0] Absolute maximum = Absolute minimum = (B) Interval = … 
calculus
2) Let g(s)= t(4−t)^1/2 on the interval [0,2]. Find the absolute maximum and absolute minimum of g(t) on this interval. Enter DNE if the absolute maximum or minimum does not exist. The absolute max occurs at t= . The absolute … 
calculus
Let f(x)=x^2+3x on the interval [1,3]. Find the absolute maximum and absolute minimum of f(x) on this interval. The absolute max occurs at x=. The absolute min occurs at x= 
calculus
Let g(s)=1/(s2) on the interval [0,1]. Find the absolute maximum and absolute minimum of g(s) on this interval. The absolute max occurs at s=. The absolute min occurs at s= 
Calculus
Let f(t)=t\sqrt{4t} on the interval [1,3]. Find the absolute maximum and absolute minimum of f(t) on this interval. The absolute max occurs at t=. The absolute min occurs at t= 
calculus
Let g(x)=(4x)/(x^2+1) on the interval [4,0]. Find the absolute maximum and absolute minimum of g(x) on this interval. The absolute max occurs at x=. The absolute min occurs at x=