F(X) = x - 4: Construct and simplify difference quotient

[chesterdg123]

Construct and simplify the difference quotient. Does this look correct. Thanks!

x(x+h)-4= x^2+HX-4

X^2-hx-4-x-4
h

x^2+hx-x
h

x^2+h
h

=x^2

 

[skeeter]

Re: F(X)=x-4

f(x) = x - 4

f(x+h) = (x+h) - 4

f(x+h) - f(x) = [(x+h) - 4] - (x - 4) = x + h - 4 - x + 4 = h

[f(x+h) - f(x)]/h = h/h = 1

 

[stapel]

F(X) = x - 4: Construct and simplify difference quotient

x(x+h)-4= x^2+HX-4

Would it be correct to assume that, contrary to standard mathematical usage, you mean the upper- and lower-case variables to stand for the same things, so, for instance, "h" and "H" are actually both the same? :shock:

(As you know from working with angles and opposite sides of triangles, variables such as "a" and "A" customarily stand for two completely different, though possibly related, items. This holds true in all other areas of mathematics as well.)

Thank you!

Eliz.