# Math Help - Tangent line approximation help?

1. ## Tangent line approximation help?

For this question: I'm having a lot of trouble figuring out f(0). Can anyone help? I know that f'(-0.5)=4 which means that f(4)=-0.5 and I know that f(-0.5)=2 which means that f'(2)=-0.5, right? But I don't know how to relate this to tangent line approximation and find f(0). Can anyone explain this to me? Thanks!

2. ## Re: Tangent line approximation help?

Originally Posted by canyouhelp
For this question: I'm having a lot of trouble figuring out f(0). Can anyone help? I know that f'(-0.5)=4 which means that f(4)=-0.5 and I know that f(-0.5)=2 which means that f'(2)=-0.5, right? But I don't know how to relate this to tangent line approximation and find f(0). Can anyone explain this to me? Thanks!
The derivative and the inverse function are two very different things. Linear approximation is as follows:

$f(x+\Delta x) \approx f(x) + f'(x)\Delta x$

In your case, $\Delta x = 0.5$

3. ## Re: Tangent line approximation help?

Originally Posted by SlipEternal
The derivative and the inverse function are two very different things. Linear approximation is as follows:

$f(x+\Delta x) \approx f(x) + f'(x)\Delta x$

In your case, $\Delta x = 0.5$
So if it's f(x)+f'(x)delta(x) then that's 2+4(.5)=4 making f(0)=4?

4. ## Re: Tangent line approximation help?

Originally Posted by canyouhelp
So if it's f(x)+f'(x)delta(x) then that's 2+4(.5)=4 making f(0)=4?
Not equal. Approximately equal. That is an approximation, not an exact answer. It is only equal if f(x) is a straight line. If it is a curve, it likely won't be accurate. 4 is the correct answer to the question.

5. ## Re: Tangent line approximation help?

Originally Posted by SlipEternal
Not equal. Approximately equal. That is an approximation, not an exact answer. It is only equal if f(x) is a straight line. If it is a curve, it likely won't be accurate. 4 is the correct answer to the question.
Oh, okay, thank you!