# Thread: compare values of ∆y and dy of function if x changes

1. ## compare values of ∆y and dy of function if x changes

Compare the values of ∆y and dy if y = f (x) = x3+x2−x+2 and x changes

(a) from 2 to 2.06 and
(b) from 2 to 2.01

2. ## Re: compare values of ∆y and dy of function if x changes

Originally Posted by asifrahman1988
Compare the values of ∆y and dy if y = f (x) = x3+x2−x+2 and x changes

(a) from 2 to 2.06 and
(b) from 2 to 2.01
Do you remember the definitions? Recall that

$\Delta y=y_2-y_1=f(x_2)-f(x_1)$

$\Delta x=x_2-x_1$

$dy=f'(x)dx$

and

$\Delta x =dx$

In problem a) you have

$x=2 \quad \Delta x =0.06$

$\Delta y =f(2.06)-f(2)$

$dy = f'(2)\cdot (0.06)$