Posted by Ren on .
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,
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