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)# 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)#**