For what value of x does the function f(x) = 4x2 - 2x + 8 assume its minimum value?
+128732 f(x) = 4x^2 - 2x + 8 .....taking the derivative and setting it to 0, we have
f ' (x) = 8x - 2 = 0
8x = 2
x = 1/4
f(1/4) = 4(1/4)^2 - 2(1/4) + 8 = 1/4 - 1/2 + 8 = 7.75
So....the minimum occurs at (1/4 , 7.75) = (.25, 7.75) .....and since this parabola turns "upward," we can be sure this is the miinimum
+128732 f(x) = 4x^2 - 2x + 8 .....taking the derivative and setting it to 0, we have
f ' (x) = 8x - 2 = 0
8x = 2
x = 1/4
f(1/4) = 4(1/4)^2 - 2(1/4) + 8 = 1/4 - 1/2 + 8 = 7.75
So....the minimum occurs at (1/4 , 7.75) = (.25, 7.75) .....and since this parabola turns "upward," we can be sure this is the miinimum
