Question

Find the difference quotient of​ f; that​ is, find StartFraction f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis Over h EndFraction comma f(x+h)−f(x) h, h not equals 0 commah≠0, for the following function. Be sure to simplify. f left parenthesis x right parenthesis equals x squared minus 2 x plus 5f(x)=x2−2x+5

Answer 1

Answer:

2x-2

Step-by-step explanation:

Given that there is a function of x as

$f(x)=x^2−2x+5$

Let us find difference quotient of f

For this, first find f(x+h)

$f(x+h)=(x+h)^2−2(x+h)+5\\=x^2+2xh+h^2-2x-2h+5\\f(x+h)-f(x) = 2xh+h^2-2h$

Divide this by h

$\frac{f(x+h)-f(x)}{h} =2x+h-2$

Take limit as h tends to 0

Difference quotient = 2x-2