{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Stitz-Zeager_College_Algebra_e-book

# 74 as a guide show that the function g whose graph is

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: = (x − 3)2 . Its distance to the origin, (0, 0), is given by d= (x − 0)2 + (y − 0)2 = x2 + y 2 = x2 + [(x − 3)2 ]2 = x2 + (x − 3)4 Since y = (x − 3)2 Given a value for x, the formula d = x2 + (x − 3)4 is the distance from (0, 0) to the point (x, y ) on the curve y = (x − 3)2 . What we have deﬁned, then, is a function d(x) which we wish to minimize over all values of x. To accomplish this task analytically would require Calculus so as we’ve mentioned before, we can use a graphing calculator to ﬁnd an approximate solution. Using the calculator, we enter the function d(x) as shown below and graph. Using the Minimum feature, we see above on the right that the (absolute) minimum occurs near x = 2. Rounding to two decimal places, we get that the minimum distance occurs when x = 2.00. To ﬁnd the y value on the parabola associated with x = 2.00, we substitute 2.00 into the equation to get y = (x − 3)2 = (2.00 − 3)2 = 1.00. So, our ﬁnal answer is (2.00, 1.00).15 (What does the y v...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online