osnomu3

2021-12-24

If $f\left(x\right)={x}^{2}-2x+3$ how do you find f(a+h)-f(a)/h?

deginasiba

Beginner2021-12-25Added 31 answers

Substitute $a+h$ and $a$ for $x$ in the formula for f(x) and simplify to find:

$\frac{f(a+h)-f\left(a\right)}{h}=2a-2+h$

$f\left(x\right)={x}^{2}-2x+3$

Then:$\frac{f(a+h)-f\left(a\right)}{h}$

$\frac{{a}^{2}+2ah+{h}^{2}-2a-2h+3-{a}^{2}+2a-3}{h}$

$=-2a-2+h$

So:

$\underset{h\to 0}{lim}\frac{f(a+h)-f\left(a\right)}{h}=\underset{h\to 0}{lim}=(2a-2+h)=2a-2$

This is the derivative of$f\left(x\right)$ at $x=a$

Then:

So:

This is the derivative of

Timothy Wolff

Beginner2021-12-26Added 26 answers

I have plotted it for you!

user_27qwe

Skilled2021-12-30Added 375 answers

thank you very much

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