Question

Use the definition of the derivative (don't be tempted to take shortcuts!) to find the derivative of the function
f(x)=7−8x+7x^2.
Then state the domain of the function and the domain of the derivative.
Note: When entering interval notation in WeBWorK, use I for ∞, -I for −∞, and U for the union symbol. If the set is empty, enter "{}" without the quotation marks.

Answer 1

got f'(x) but cant get domains

Answer 2

@Algebraic! could you help me?

Answer 3

14x-8 is derivative

Answer 4

\[\lim_{h \rightarrow0} \frac{ f(x+h) -f(x) }{h }\]

Answer 5

\[\lim_{h \rightarrow0} \frac{ 7(x+h)^2 -8(x+h) +7 -(7x^2 -8x +7) }{h }\]

Answer 6

expand (x+h)^2 and then simplify the expression...

Answer 7

when it's simplified so that there's no longer a problem with taking the limit as h->0, then take the limit by substitution.

Answer 8

is this the way you did it?

Answer 9

ya and i got x=4/7

Answer 10

14x-8 ...?

Answer 11

try it; you should get the derivative.. since that's what this expression is...

Answer 12

ya i got 14x-8 for the derivitave

Answer 13

ok, the domain is all x

Answer 14

ya \[x \neq4/7\]

Answer 15

why's that?

Answer 16

(-inf,4/7)U(4/7,inf)

Answer 17

because if you plug that in y=0

Answer 18

that would make it a root. it's not a root of either the function or the derivative though, so not sure where you're getting it.
roots are part of the domain anyway... I really don't have any idea what you did so far on this problem... did you use the limit definition to find the derivative?

Answer 19

idk im super confused

Answer 20

the function is a parabola, so there's no restriction on x values it can have...
the derivative is a line so there's no restriction on x values it can have either...

Answer 21

ok so how i ind domain of fx