Question

If f is a function such that lim x->a f(x)-f(a)/x-a =7 , then which of the following statements must be true?
a. f(a) = 7
b. f(x) is continuous at x = 7
c. the linear approximation for f(x) at x = a is 7
d. f '(a) = 7

Answer 1

i think its the derivative of a

Answer 2

is that d?

Answer 3

is that suppose to say
\[\lim_{x \rightarrow a}\frac{f(x)-f(a)}{x-a}=7 ?\]

Answer 4

yes

Answer 5

Here are a few hints:
1) recall definition of derivative
2) if derivative exist at x=a, then the function is continuous at x=a
3) the linear approximation to f(x) at x=a is given by L(x)=f'(a)(x-a)+f(a) and what happens if you use the linear approximation to evaluate L(a)

Answer 6

the linear approximation for f(x) at x = a is 7

Answer 7

L(x)=f'(a)(x-a)+f(a)

Finding L(a) <--we are finding the linear approximation at x=a
L(a)=f'(a)(a-a)+f(a)
L(a)=?

Answer 8

If you are saying "the linear approximation for f(x) at x = a is 7" is your answer, I'm kind asking you how do you know that f(a)=7 since the linear approximation to f at x=a is L(a)=f(a) we do not know f(a)=7 so we cannot say this choice

Answer 9

So use the other two hints given

Answer 10

what is your definition of derivative?

Answer 11

you are almost done weeding out the false statements

Answer 12

I must go
good luck