AP Calculus BC Practice Exam 2 407
- Letf be a function with the following
properties.
x f(x) f′(x) f′′(x) f′′′(x)
0 1 1 2 6
2 − 1 1 − 2 6
Which of the following is the third-degree
Taylor polynomial forf aboutx=2?
(A) 1 +x+x^2 + 2 x^3
(B) x− 3 − 2 (x− 2 )^2 + 6 (x− 2 )^3
(C) − 3 +x−(x− 2 )^2 +(x− 2 )^3
(D) − 3 +x−(x− 2 )^2 + 2 (x− 2 )^3
y
x
f′′
- The graph off′′, the second derivative offis
shown above. The graph off′′has horizontal
tangents atx=−2 andx=2. For what values
ofxdoes the graph of the functionfhave a
point of inflection?
(A) −4, 0 and 4
(B) −2, 0 and 2
(C) −4 and 4 only
(D) 0 only
- Given the infinite series
∑∞
k= 1
√
k
kn
, what are all
values ofnfor which the series converges?
(A) n>
1
2
(B) n> 1
(C) n>
3
2
(D) n≥
3
2
- If f(x)is continuous andf(x)>0on[0, 4]
and twice differentiable on(0, 4)such that
f′(x)>0 and f′′(x)>0, which of the
following has the greatest value?
(A)
∫ 4
0
f(x)dx
(B) Left Riemann sum approximation of∫
4
0
f(x)dxwith 4 subintervals of equal
length
(C) Right Riemann sum approximation of∫
4
0
f(x)dxwith 4 subintervals of equal
length
(D) Midpoint Riemann sum approximation
of
∫ 4
0
f(x)dxwith 4 subintervals of
equal length
- Which of the following is an equation of the
tangent line to the curve described by the
parametric equationsx=tandy=t^2 when
t=4?
(A) y= 8
(B) y= 2 x+ 8
(C) y= 8 x− 16
(D) y= 8 x+ 16
- Let fandgbe differentiable functions such
thatg(x)=f−^1 (x).Iff( 2 )=4,f( 3 )=9,
g′( 4 )=
1
4
andg′( 9 )=
1
6
, what is the value of
f′( 3 )?
(A) 3
(B) 4
(C) 6
(D) 9
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