Let f(x)=√(x−18) and use the Linear Approximation to this function at a=43 with Δx=0.4 to estimate f(43.4)−f(43)=Δf≈df=
Well after I did all the work I got .1x+.7 and then I plugged in 43.4 and 43 and typed in the answer of 5.04 and 5 and still did not get it right any clues?

Question

Let f(x)=√(x−18) and use the Linear Approximation to this function at a=43 with Δx=0.4 to estimate f(43.4)−f(43)=Δf≈df=	 
Well after I did all the work I got .1x+.7 and then I plugged in 43.4 and 43 and typed in the answer of 5.04 and 5 and still did not get it right any clues?

anonymous · Answer

@ranga think you could help me with this one?

ranga · Answer

Are you allowed to take derivatives?

anonymous · Answer

Yea thats what I did

ranga · Answer

f(x) = (x - 18)^(1/2)
f'(x) = 1/2(x - 18)^(-1/2)
f'(x) at x = 43 is:
f'(43) = 1/2(43-18)^(-1/2) = 1/(2 * 25^(1/2)) = 1/10 = 0.1

ranga · Answer

f(43.4)−f(43) / delta_x approximately equal to df/dx at x = 43 = 0.1
f(43.4)−f(43)  approx = 0.1 * delta_x = 0.1 * 0.4 = 0.04

anonymous · Answer

Oh awesome thanks, I guess I did mine a different way but your way was right!

ranga · Answer

alright. yw.