Use linear approximation to estimate f (5.1) given that f(5) =...

Question

Use linear approximation to estimate f (5.1) given that f(5) = 10 and f'(5) = -2.

Accepted Answer

Hi everyone, let's take a look at this practice problem dealing with linear approximation. This problem says, given H 2 is equal to 4 and H2 is equal to -1, use linear approximation to find the estimated value of H of 2.1. We have 4 possible choices as our answers. For choice A, we have 2.8. For choice B, we have 4.1. For choice C, we have 3.9, and for choice D, we have 4.2. Now we're we're asked to estimate the value of H of 2.1 using a linear approximation. To recall for a linear approximation, that we have L of X. is equal to H of A. Plus H A multiplied by the quantity of X minus A. So in our case here, A is going to be equal to 2, since we were given H of 2 and H2, and X is going to be equal to 2.1, since we're looking for the value of H of 2.1. So substituting these values into our expression, we will have L of 2.1. And that's gonna be equal to H of 2, which we were given in the problem, as having a value of 4. And then we'll have plus H2, which we're told and the problem was equal to -1. We'll have -1, multiplied by the quantity of X minus A, which is 2.1 minus 2. So we can simplify this expression, this is going to be equal to. 4 minus. 0.1, which is going to be equal to 3.9. So this here is the answer that we're looking for. And if we compare that to our answer choices, we see that the correct answer choice corresponds to answer choice C. So, I hope that this explanation has been useful, and I'll see you in the next video.

Use linear approximation to estimate f (5.1) given that f(5) = 10 and f'(5) = -2.

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