Difference Quotient: find f(a), f(a+h), etc for f(x)=-7/x-3

[NadroJV13]

Findf(a), f(a+h) and the difference quotient for the fuction goven below, where h does not equal zero.

f(x)= -7/x-3

f(a)= -7/a-3

f(a+h)= -7/(a+h)-3

f(a+h)-f(a) = -7/(a+h)-3-(-7/a-3) all over h
h


I could use help solving this

 

[fasteddie65]

Re: Difference Quotient

Findf(a), f(a+h) and the difference quotient for the fuction goven below, where h does not equal zero.

f(x)= -7/x-3

f(a)= -7/a-3

f(a+h)= -7/(a+h)-3

f(a+h)-f(a) = -7/(a+h)-3-(-7/a-3) all over h
h

[-7/(a + h) - 3 -(-7/a - 3)]/h

Rationalize the numerator:

[-7/(a + h) - 3 -(-7/a - 3)]/h • a(a + h)/[a(a + h)] =

[-7a - 3a(a + h) + 7(a + h) + 3a(a + h)]/[ah(a + h)] =

[-7a - 3a^2 - 3ah + 7a + 7h + 3a^2 + 3ah]/[ah(a + h)] =

7h/[ah(a + h)] = 7/[a(a + h)] --> 7/a^2 as h --> 0

 

[fasteddie65]

Re: Difference Quotient

I just realized that your syntax may have been unclear.

Is the function f(x) = -7/(x - 3) or -7/x - 3?

 

[NadroJV13]

Re: Difference Quotient

f(x)= -7/x-3