find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x…

find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x - values at which they occur.\nf(x)=2x - 5\n(a) 0,4 (b) -3,2\n(a) the absolute maximum value is (square) at (x=square).\n(use a comma to separate answers as needed.)\nthe absolute minimum value is (square) at (x=square).\n(use a comma to separate answers as needed.)\n(b) the absolute maximum value is (square) at (x=square).\n(use a comma to separate answers as needed.)\nthe absolute minimum value is (square) at (x=square).\n(use a comma to separate answers as needed.)

find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x - values at which they occur.\nf(x)=2x - 5\n(a) 0,4 (b) -3,2\n(a) the absolute maximum value is (square) at (x=square).\n(use a comma to separate answers as needed.)\nthe absolute minimum value is (square) at (x=square).\n(use a comma to separate answers as needed.)\n(b) the absolute maximum value is (square) at (x=square).\n(use a comma to separate answers as needed.)\nthe absolute minimum value is (square) at (x=square).\n(use a comma to separate answers as needed.)

Answer

Explanation:

Step1: Analyze the function ( f(x) = 2x - 5 )

Since the function ( f(x)=2x - 5 ) is a linear function with a slope ( m = 2>0 ), it is a strictly increasing function.

Step2: Evaluate the function at the endpoints of the intervals

For interval ([0,4])

  • When ( x = 0 ), ( f(0)=2\times0 - 5=-5 )
  • When ( x = 4 ), ( f(4)=2\times4 - 5=8 - 5 = 3 )

For interval ([-3,2])

  • When ( x=-3 ), ( f(-3)=2\times(-3)-5=-6 - 5=-11 )
  • When ( x = 2 ), ( f(2)=2\times2 - 5=4 - 5=-1 )

Answer:

(A) The absolute maximum value is (3) at (x = 4\). The absolute minimum value is (-5) at (x = 0). (B) The absolute maximum value is (-1\) at (x = 2).( ) The absolute\ minimum value is (-11\) at (x=-3).