# Linear approximation help.

• Nov 20th 2012, 07:15 AM
Mathinik
Linear approximation help.
• Nov 20th 2012, 08:11 AM
skeeter
Re: Linear approximation help.
the tangent line, $y = -3x+7$ , serves as an approximation of function values close to x = 2.

$f(x) \approx -3x+7$ for values of x close to x = 2.

$f(2.1) \approx -3(2.1)+7$

$f(1.98) \approx -3(1.98)+7$

... as far as an "over" or "under" estimate, look at the tangent line and the concavity of f(x) on both sides of x = 2.

... the tangent line and f(x) have the same value at x = 2. What do you think happens to the accuracy of the approximation as x gets farther away from x = 2?
• Nov 20th 2012, 08:49 AM
Mathinik
Re: Linear approximation help.
Book has f(2.1),overestimate and f(1.98), underestimate. That part I don't get, should it be the other way? I get that the second approximation, f(1.98), is better because it is closer to 2. The over and under is throwing me off! Thanks for your reply.
• Nov 20th 2012, 08:59 AM
skeeter
Re: Linear approximation help.
"book" has it backwards w/r to over and underestimates