Barrons AP Calculus

(Marvins-Underground-K-12) #1
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Given   two twice-differentiable    functions,  f(x)    and g(x).   The table   above
gives values for f(x) and g(x) and their first and second derivatives at x =


  1. Find .


−3
1
2
nonexistent
A differentiable function has the values shown in this table:

Estimate    f   ′(2.1).
0.34
1.56
1.70
1.91

If      is  approximated    using   various sums    with    the same    number
of subdivisions, and if L, R, and T denote, respectively, left Riemann
Sum, right Riemann Sum, and trapezoid sum, then it follows that
R ≤ A ≤ T ≤ L
R ≤ T ≤ A ≤ L
L ≤ T ≤ A ≤ R
L ≤ A ≤ T ≤ R

The number  of  vertical    tangents    to  the graph   of  y^2     =   x   −   x^3     is
3
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