Let f be a differentiable function such that f(3) = 2 and f'(3) = 5....

e3r2a1cakCh7

e3r2a1cakCh7

Answered

2022-12-01

Let f be a differentiable function such that f(3) = 2 and f'(3) = 5. If the tangent line to the graph of f at x = 3 is used to find an approximation to a zero of f, that approximation is?

Answer & Explanation

ysik92ASw

ysik92ASw

Expert

2022-12-02Added 13 answers

Find an approximate value of a zero of f(x) near a=3. That is to say, you're looking for some value c such that f(c)=0, but all you have at your disposal is the linear approximation to the function.
f ( x ) f ( 3 ) + f ( 3 ) ( x 3 ) f ( x ) 2 + 5 ( x 2 ) f ( x ) 5 x 8
You know that if c is a zero of , f(c)=0, so you get
f ( c ) 5 c 8 0 = 5 c 8 5 c = 8 c = 8 5 = 1.6An approximate zero of f(x) is x=1.6.

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