Asked by Anonymous
Find the linearization L(x) of the function at a.
f(x) = x^1/2, a = 25
f(x) = x^1/2, a = 25
Answers
Answered by
Steve
What you want is a line that approximates the curve at some point (and, by extension, in some small interval).
f'(x) = 1/(2√x)
f'(25) = 1/10
So, you want the line through (25,5) with slope = 1/10
(y-5) = 1/10 (x-25)
y = x/10 + 5/2
If you restrict your interval of x-values, you can show that the line is as close as you want to the curve in that interval.
f'(x) = 1/(2√x)
f'(25) = 1/10
So, you want the line through (25,5) with slope = 1/10
(y-5) = 1/10 (x-25)
y = x/10 + 5/2
If you restrict your interval of x-values, you can show that the line is as close as you want to the curve in that interval.
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