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Numerade Educator

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Problem 6 Medium Difficulty

Find the linear approximation of the function $ g(x) = \sqrt [3]{1 + x} $ at $ a = 0 $ and use it to approximate the numbers $ \sqrt [3]{0.95} $ and $ \sqrt [3]{1.1}. $ Illustrate by graphing $ g $ and the tangent line.

Answer

$L(x)=1+\frac{1}{3} x, \quad \sqrt[3]{0.95} \approx 0.9833, \quad \sqrt[3]{1.1} \approx 1.033$

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Video Transcript

Okay, Jim zero is the cube root of one plus zero, which is one therefore, G prime of acts is 1/3 times. Now we're playing in zero. So one plus zero to the negative to over three simplifies to 1/3 plug into the blender or ization formula with sequels one plus 1/3 axe. So now we have one plus X equals 0.95 they're for ox equals negative 0.5 Therefore, we have one plus 1/3 times negative 0.5 0.9833 You know The cube root of 1.11 plus X is 1.1 an ax 0.11 plus 1/3 time's Your 0.1 is one point 1.3 three.