Posted by **Ren** on Wednesday, November 7, 2012 at 9:49pm.

f(x)=x^3-3x^2+3x+1 near 2 (at a=2)

A. Use Linear approximation to approximate.

b.is this underestimate or overestimate? Justify answer.

C.Approximate f(2.25) using the linear approximation and compare the answer with the exact value.

Thanks.

- Calculus(Urgent help) -
**Steve**, Thursday, November 8, 2012 at 12:01am
f'(x) = 3x^2 - 6x + 3

f''(x) = 6x - 6

f''(2) > 0, so the graph is concave up at x=2. So, a linear approximation will underestimate f(x)

f'(2) = 3

f(2) = 3

the line through (2,3) with slope 3 is

y = 3(x-2)+3= 3x-3

y(2.25) = 3.75

f(2.25) = 3.953

the line underestimates

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