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• jaredjjj
In summary, the conversation discusses solving a linear approximation question and determining if the value is an over or under estimate. The formula f'(x)=sqrt(x^2+7) is used to find the value, and the conversation also mentions the sign of f''(3) and its significance in understanding the behavior of f(x) at x=3.
jaredjjj
Have I solved this linear approximation question correctly?

yes, $f(2.8) \approx -2.8$

now, how to determine if that value is an over or under estimate?

skeeter said:
yes, $f(2.8) \approx -2.8$

now, how to determine if that value is an over or under estimate?
To answer the second half do I have to use the formula f'(x)=sqrt(x^2+7) which would mean -2.8 would be approximately equal to 3.852 which is the same as 2.8.

jaredjjj said:
To answer the second half do I have to use the formula f'(x)=sqrt(x^2+7) which would mean -2.8 would be approximately equal to 3.852 which is the same as 2.8.

?

The linear approximation is a line tangent to $f(x)$ at the point $(3,-2)$.

What does the sign of $f''(3)$ tell you about the behavior of $f(x)$ at $x=3$ ?

1. What is linear approximation?

Linear approximation is a mathematical technique used to approximate the value of a function at a particular point by using the tangent line at that point. It is based on the concept of local linearity, where a small portion of a curve can be approximated by a straight line.

2. How is linear approximation different from other methods of approximation?

Linear approximation is different from other methods of approximation because it uses a linear function to approximate a non-linear function. This allows for a simpler and more accurate approximation compared to other methods.

3. What is the formula for linear approximation?

The formula for linear approximation is y = f(a) + f'(a)(x-a), where f(a) is the value of the function at the point a, f'(a) is the derivative of the function at the point a, and x is the point at which the function is being approximated.

4. When should linear approximation be used?

Linear approximation should be used when a function is too complex to be evaluated directly, but a good approximation is needed. It is also useful when finding the values of functions at points that are close to the known values, as the linear approximation is most accurate near the point of approximation.

5. How can I check if my answer using linear approximation is accurate?

You can check the accuracy of your answer using linear approximation by comparing it to the actual value of the function at the given point. If the difference between the two values is small, then the linear approximation is considered to be accurate.

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