Answer should be up to one decimal place only.

f(x) = x^2 - 2 on [0,3]
asked Aug 12, 2017 in Calculus Answers by skeptic (160 points)

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Best answer

When x=0, f(0)=x^2-2=-2 and f(3)=9-2=7. So there is a change of sign between x=0 and x=3, implying that the root lies in between.

The average or midway position is x=1.5 and f(1.5)=2.25-2=0.25. Therefore the root lies between 1.5 and 0.

The midway position is 0.75 and f(0.75)=0.5625-2=-1.4375. So the root lies between 0.75 and 1.5, i.e., 1.125 as the midway point. And f(1.125)=-0.734375. The midway point including the root is (1.125+1.5)/2=1.3125.

f(1.3125)=-0.27734375, meaning that the root lies between 1.3125 and 1.5, with a midpoint of 1.40625, and f(1.40625)<0, so the root lies in the interval [1.40625,1.5], the midway point being 1.453125, and f(1,453125)>0 so the root lies in the interval [1.40625,1.43125], the midway point of which is 1.41875. We can see that to one decimal place the root is 1.4, because both extremes of the limit give us 1.4.

answered Aug 12, 2017 by Rod Top Rated User (550,780 points)
selected Aug 12, 2017 by skeptic
Thank you Sir Rod!

Hoping to help for my other post. Thanks again!

Related questions

Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
81,193 questions
85,287 answers
68,722 users