Compare the values of ∆y and dy if y = f (x) = x^{3}+x^{2}−x+2 and x changes

(a) from 2 to 2.06 and

(b) from 2 to 2.01

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- Mar 17th 2013, 01:29 AMasifrahman1988compare values of ∆y and dy of function if x changes
Compare the values of ∆y and dy if y = f (x) = x

^{3}+x^{2}−x+2 and x changes

(a) from 2 to 2.06 and

(b) from 2 to 2.01 - Mar 17th 2013, 04:40 AMTheEmptySetRe: compare values of ∆y and dy of function if x changes
Do you remember the definitions? Recall that

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

$\displaystyle \Delta x=x_2-x_1$

$\displaystyle dy=f'(x)dx$

and

$\displaystyle \Delta x =dx$

In problem a) you have

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

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

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