College Algebra

Question

f(x) = 2x² − 14x + 6 find the minimum or maximum value of f.

Answer 1

take the first derivative of f and set it equal to zero

f'(x) = 4x-14 = 0

then solve for x

4x = 14

x = 14/4= 7/2

substitute x= 7/2 into the original equation for the minimum value

f(7/2) = 2(7/2)^2 - 14(7/2) + 6 = 49/2 - 49 + 6 = -18 1/2

maximum value is infinity

the function is an upward opening parabola with vertex at (7/2, - 37/2) as the minimum point.

It opens upwards approaching infinity, when x approaches infinity. The greater x, the greater f

also x approaching negative infinity will make f approach positive infinity as well.