Math  /  Calculus

Question Find the linear approximation to g(x)=x4g(x)=\sqrt[4]{x} at x=2x=2. Use it to approximate 34\sqrt[4]{3} and 104\sqrt[4]{10}. Compare to exact values. Analyze percent error and accuracy.

Studdy Solution
Discuss why one approximation is much closer to the exact value than the other.
The linear approximation is more accurate near the point of tangency (x=2x = 2) and becomes less accurate as we move away from this point. Since 33 is closer to 22 than 1010 is, the approximation for 34\sqrt[4]{3} is more accurate than the approximation for 104\sqrt[4]{10}.

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