Sorry about the mistakes. Still learning how to do linear approximation.I do have two concerns. First you wrote f(x) = f(3) which is not true. 2ndly you wrote f(2.8) = .... whis is also not true. At best f(2.8) ~ ....
Equal signs must be valid!
I do have two concerns. First you wrote f(x) = f(3) which is not true. 2ndly you wrote f(2.8) = .... whis is also not true. At best f(2.8) ~ ....
Equal signs must be valid!
Your first mistake had nothing to do with linear approximation. Except for a constant function, f(x) depends on x (ie it has different values which depends on x) where f(3) is a real number, a constant. f(x)=f(3) is not true (unless f(x) is a constant). Your other mistake has to do with using equal signs (again!). As you wrote at the top of you page, f(x) ~ =..... which is correct. Then when you APPROXIMATED f(2.8) you wrote f(2.8) =...Sorry about the mistakes. Still learning how to do linear approximation.
Either you are saying that -2.8 is the same as 3.853 or you are saying that 3.852 is the same as 2.8. Why would you say that! Those number are not equal to one another.To answer the second half do I have to use the formula f'(x)=sqrt(x^2+7) which would mean -2.8 would be approximately equal to 3.852 which is the same as 2.8.
The derivative is a limit so that: \(f'(a) = \mathop {\lim }\limits_{\Delta x \to 0} \dfrac{{f(a + \Delta x) - f(a)}}{{\Delta x}}\quad \Rightarrow \quad f(a + \Delta x) \approx f'(a)\Delta x + f(a)\)