Question

Find: (f(x+c)-f(x))/c

If f(x) = 2x^3-5x

Answer 1

can you evaluate f(x+c) if given f(x)=2x^3-5x
hint: just replace the old input x wherever you see with the new input (x+c)

Answer 2

@freckles how would you incorporate c if we aren't given a value?

Answer 3

example:
if f(x)=x^2 then f(x+c)=(x+c)^2

Answer 4

wherever you see x you replace it with (x+c)

Answer 5

if f(x)=5-x+x^2
then f(x+c)=5-(x+c)+(x+c)^2

Answer 6

so if f(x)=2x^3-5x
then f(x+c)=?

Answer 7

once you find f(c+h)
we can plug into difference quotient when you are ready for that

Answer 8

@freckles 2(x+c)^3-5(x+c) ?

Answer 9

great! \[\frac{f(x+c)-f(c)}{h}=\frac{[2(x+c)^3-5(x+c)]-[2c^3-5c]}{h}\]
now this is the part where we multiply everything out on the top and see if anything cancels in the top

Answer 10

oops that h down there is suppose to be a c by the way

Answer 11

and i read your problem wrong f(c) is f(x) lol

Answer 12

Okay that's what I thought lol!

Answer 13

\[\frac{f(x+c)-f(x)}{c}=\frac{2(x+c)^3-5(x+c)]-[2x^3-5x]}{c}\]

Answer 14

now we still need to multiply stuff out on the top and see if anything cancels on the top

Answer 15

if i was multipying out (x+c)^3 i would refer to my handy dandy pascal's triangle