Posted by Ren on Wednesday, November 7, 2012 at 9:49pm.
f(x)=x^33x^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(x2)+3= 3x3
y(2.25) = 3.75
f(2.25) = 3.953
the line underestimates
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