Find the difference quotient F (X+H) - F (X) / h for the following function F(x) = x^2-9x

Question

Find the difference quotient F (X+H) - F (X) ALL OVER H.

 

Using function F (x) = x^2-9x

 

 

 

Getting stumped ?

 

Thank You ....

Answer 1

f(x)= x^2 - 9x

f(x+h) = (x+h)^2 - 9(x+h) = x^2 +2xh+h^2 -9x-9h

f(x+h)-f(x) = x^2+2xh+h^2-9x-9h -x^2+9x

the x^2 and x terms cancel leaving

f(x+h)-f(x) = 2xh+h^2 -9h

[f(x+h)-f(x)]/h = 2x+h -9

if you took the limit as h approaches zero then the limit of [f(x+h) -f(x)]/h would approach 2x +0 -9 = 2x-9

which is the derivative of f(x)=x^2-9x or f'(x)=2x-9