Question

Find and simplify the difference quotient of f, f(x+h) + f(x) / h, h is not equal to 0, for the function.

f(x) = 4x + 9

Answer 1

should be f(x+h) - f(x) / h right?

Answer 2

ok, thx

Answer 3

No, thank you

Answer 4

\[\Large f(x) = 4x + 9\]


\[\Large f(x+h) = 4(x+h) + 9\]


\[\Large f(x+h) = 4x+4h + 9\]

--------------------------------

\[\Large \frac{f(x+h)-f(x)}{h}\]


\[\Large \frac{(4x+4h + 9)-(4x+9)}{h}\]


\[\Large \frac{4x+4h + 9-4x-9}{h}\]


\[\Large \frac{(4x-4x)+4h + (9-9)}{h}\]


\[\Large \frac{\cancel{(4x-4x)}+4h + \cancel{(9-9)}}{h}\]


\[\Large \frac{4h}{h}\]


\[\Large \frac{4\cancel{h}}{\cancel{h}}\]


\[\Large 4\]
So \[\Large \frac{f(x+h)-f(x)}{h}=4 \ \text{where} f(x) = 4x+9\]

Answer 5

So answer is choice C

Answer 6

Thanks

Answer 7

np