Question

If f(x)= 4x+9 , find f(a+h)-f(a)/h

Answer 1

first step is to find (carefully )
\[f(a+h)\] which will be
\[4(a+h)+9=4a+4h+9\]

Answer 2

from that, subtract \(f(a)=4a+h\) in other words, compute
\[4a+4h+9-(4a+9)\]

Answer 3

let me know what you get, there is only one more step after that

Answer 4

do i have to distribute the - ?

Answer 5

oh yes!

Answer 6

for it to be 4a+4h+9-4a-9

Answer 7

that is the first step yes, then do the actual subtraction, i.e. combine like terms

Answer 8

so that means it is 4h ?

Answer 9

yes

Answer 10

and finally, divide that by \(h\) and what do you get?

Answer 11

4:)

Answer 12

yes, zactly
this tells you that if \(f(x)\) is a line like \(f(x)=mx+b\) then
\[\frac{f(a+h)-f(a)}{h}=m\] the slope

Answer 13

aka "the change in y over the change in x"
if \(f\) is not a line, then it is something else

Answer 14

oh okay ! :D Thank you so much !:) @satellite73

Answer 15

yw

Answer 16

@satellite73 :)

Answer 17

:) to you as well