Part b. I need help with. I don't get it! Please help!

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- Nov 20th 2012, 07:15 AMMathinikLinear approximation help.
Part b. I need help with. I don't get it! Please help!

- Nov 20th 2012, 08:11 AMskeeterRe: Linear approximation help.
the tangent line, $\displaystyle y = -3x+7$ , serves as an approximation of function values close to x = 2.

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

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

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

... 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 AMMathinikRe: 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 AMskeeterRe: Linear approximation help.
"book" has it backwards w/r to over and underestimates