Question

The polynomial function f is defined by f(x)=2x³-7x² +5x-2.

Use the ALEKS graphing calculator to find all the points (x, f (x)) where there is a local maximum.
Round to the nearest hundredth.
If there is more than one point, enter them using the "and" button.
(x, f(x)) = D
and
X
5

Answer 1

f(x) = 2x³ - 7x² + 5x - 2

f'(x) = 6x² - 14x + 5 = 0

x = (14 ± √((-14)² - 4(6)(5)))/(2×6)

= (14 ± √76)/12

= .44, 1.89

f((14 - √76)/12) = -.98

f((14 + √76)/12) = -4.05

The local maxima are approximately

(.44, -.98) and (1.89, -4.05).