please help me with this

Question

Find the difference quotient of​ f; that​ is, find f(x+h)-f(x) , h =/ 0,

for the following function: f(x)=-6x+5 h

Answer 1

Well, if f(x)=-6x+5 then f(x+h)=-6(x+h)+5 . You see, we just replace all instances of x with (x+h) whenever we see f(x+h).

So now, plugging into the difference quotient formula, we have [-6(x+h)+5 - (-6x+5)]/h

Do the algebra here and then the Hs should cancel in such a way that you get a nice answer.

Answer 2

f(x) = -6x + 5

[f(x+h) - f(x)] / h = [-6(x+h) + 5 - (-6x + 5)] / h = -6h / h = -6

Answer 3

f(x) = -6x + 5

f(x+h) = -6(x+h) + 5 = -6x - 6h + 5

f(x+h) - f(x) = -6x - 6h + 5 - (-6x + 5) = -6x - 6h + 5 + 6x - 5 = 6h

[f(x+h) - f(x)]/h = -6h/h = -6