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?

Question

Let f be a differentiable function such that f(3) = 2 and f&#039;(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?

ysik92ASw · Accepted Answer

Find an approximate value of a zero of f(x) near a=3. That is to say, you&#039;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  −  8You 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.