Question

Explain local linear approximation and how to do it please?

Answer 1

Of one variable or two? Are you in Cal I?

Answer 2

I think it's 1 variable. Here's the question:
For the function f, f ' (x)=2x+1 and f(1) = 4. What is the approximation for f(1.2) found by using the line tangent to the graph of f at x=1?
I'm in AP Calc AB

Answer 3

Because it is a AP question, there is a lot of trickery involved rather than a straightforward question. You can start of by finding f(x). I imagine that would be the integral of f'(x)=2x+1

Answer 4

I imagine f(1)=4 should have been f'(1)=4?

Answer 5

no it just says f(1) = 4.
I got x^2 + x + C as f(x) through integration. I remember you're supposed to do local linear approximation to find C, but I don't remember how & I can't find my notes from that day.

Answer 6

Local linear approximation would be f(1)+f'(1)(1)(1.2-1)

Answer 7

Decoding that: evaluate f at one, add to (f' evaluated at one, multiplied by 1.2-1). I accidentally wrote an extra (1) above.

Answer 8

So 4.6? Thanks so much.

Answer 9

I think there is a clue in there find C. f(1)=4. so therefore (1^2) +1 + C=4 Solve for C

Answer 10

Check your answer. Redo everything with the value f(x)=x^2+x+2 (Now that we know the value of C.