a Determine , without graphing , whether the function has a minimum value or a maximum value. Find the minimum or maximum value and determine where it occurs .

Question

a Determine , without graphing , whether the function has a minimum value or a maximum value. Find the minimum or maximum value and determine where it occurs .

f(x) =2x^2-4x-2

A) the function has a ___ value

B) the minimum/maximum value is___ it occurs at x=__

Answer 1

2x^2 -4x - 2

take the derivative, set =0

4x -4 =0

4x =4

x =1

plug into the original equation

2(1)^2 -4(1) -2 = 2-4-2 =-4

(1,-4) is the minimum point = vertex of the upward opening parabola

Answer 2

f(x) = 2x² - 4x - 2

This is quadratic with a>0, so f(x) is facing up, so it must have a minimum

The minimum will be at the vertex

the x coordinate of the vertex = -b/2a (here a = 2, b = -4, c = -2) so you can find that

then substitute this x value into f(x) to find the minimum value

[ you can check your answers by graphing on Desmos ]