Approximate the number $4 sqrt(1.1)$ using the tangent line approximation to the curve y = f(x) when x is near the target 1.1? hint use: $f(x) ≈ f(a) + f′(a)(x−a)$

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Answer 1 · 2016-07-14T23:07:53

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Define $f(x) = 4sqrt(x)$ . According to the tangent line given as

$y = f(1.1)+f'(1.1)(x-1.1)$

and substituting $f'(1.1) =2/sqrt(1.1)$ we have

$y = 4sqrt(1.1)+2/sqrt(1.1)(x-1.1)$

Attached a comparative plot with $y = 4sqrt(x)$ in blue and
$y = 4sqrt(1.1)+2/sqrt(1.1)(x-1.1)$ in red, near the point $x = 1.1$

enter image source here

Approximate the number 4 sqrt(1.1)4 sqrt(1.1) using the tangent line approximation to the curve y = f(x) when x is near the target 1.1? **hint use: f(x) ≈ f(a) + f′(a)(x−a)f(x) ≈ f(a) + f′(a)(x−a)**