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3.8, #2, Given Problem.
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Find the linearization of L(x) of the
function at a.
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Problem #2, Lesson 3.8 |
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We first find the general derivative. |
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We find the derivative at x = 1. Now we have our slope. |
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We use the linearization formula to calculate the linearization. |
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Alternate Solution:
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Begin with the slope-intercept form of a line. |
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We use the slope of 1 found above. |
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Substitute in the given point where we are to find the approximation. (1, 0) |
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This way, we arrive at the same linear approximation equation. |
3.8, #6, Given Problem.
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Problem #6, Lesson 3.8 |
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We begin by differentiating the function g(x). |
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Now we find the slope at a. |
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Using our slope, we substitute into the slope-intercept form of a line. |
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We can then solve for b. |
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Here is the linearization formula. |
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To find the linearization at 0.95, we need x to be -.05. We therefore find our approximation for the cube root of 0.95. |
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To find the linearization at 1.1, we need x to be .1. We therefore find our approximation for the cube root of 1.1. |
3.8, #16, Given Problem.
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Problem 16, Lesson 3.8 |
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Here is our linearization. |
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(a) Now we have our approximation for x = 1.1 |
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This tells us that the original function (even though we don't know its equation is concave up at x = 1.1. Therefore our estimate must be below the actual value. |
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