Please help ASAP sirs thanks alot

asked Jun 11 in Calculus Answers by Joseph

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

1. First we find the gradient (slope) of the curve at x=a=2.

To do this we differentiate the function: f'(x)=-2x=-4 when x=2.

So we can write the equation of the line as y=-4x+b where b is a constant and we’ve used the slope of the tangent at x=2 to find the slope of the line.

We know the line must pass through the point where x=2 and f(2)=12-4=8. So the line must pass through the point (2,8). If we put these into the equation of the tangent line we can find b:

8=-4×2+b, so b=8+8=16 and y=-4x+16. So the blanks are -4 and 16 for y=L(x).

2. x=2.1 is close to x=2 so we can approximate f(2.1) using the line equation from (1): y=-4(2.1)+16=-8.4+16=7.6.

3. The exact value of f(2.1) is 12-2.1²=12-4.41=7.59. See how close the approximation was? The error is (7.60-7.59)/7.59=0.01/7.59=0.001318 approximately. Multiply by 100 to get the percentage error and we get 0.1318% (too high).

answered Jun 11 by Rod Top Rated User (545,980 points)

Related questions

Welcome to MathHomeworkAnswers.org, 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!
81,126 questions
85,200 answers
2,143 comments
68,618 users