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omojay1257

28.10.2021

Mathematics

The linear approximation to f(x) near x=16 is

L(x)=f(16)+f'(16)(x-16)

We have

$f(x)=\sqrt x\implies f(16)=4$

$f'(x)=\dfrac1{2\sqrt x}\implies f'(16)=\dfrac18$

$\implies L(x)=4+\dfrac18(x-16)=\dfrac x8+2$

Then

$f(16.2)\approx L(16.2)\iff\sqrt{16.2}\approx\dfrac{16.2}8+2$

$\implies\boxed{\sqrt{16.2}\approx4.025=\dfrac{161}{40}}$

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