Question
Learning. If a person learns $y$ items in $x$ hours, as given approximately by $$ y=52 \sqrt{x} \quad 0 \leq x \leq 9 $$ what is the approximate increase in the number of items learned when $x$ changes from 1 to 1.1 hours? From 4 to 4.1 hours?
Step 1
This function can also be written as $y = 52x^{1/2}$. Using the power rule for differentiation, we get: \[y' = \frac{1}{2} \cdot 52x^{-1/2} = 26x^{-1/2} = \frac{26}{\sqrt{x}}.\] Show more…
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If a person learns $y$ items in $x$ hours, as given approximately by $$ y=52 \sqrt{x} \quad 0 \leq x \leq 9 $$ what is the approximate increase in the number of items learned when $x$ changes from 1 to 1.1 hours? From 4 to 4.1 hours?
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