AP CALC BC REIVEW MCQ
If y=xy+x^2+1, then when x=-1, dy/dx is
-1/2
let f be the function given by f(x) = 3-2x. if g is a function with derivative given by g'(x) = f(x)f'(x)(x-3), on what intervals is g increasing?
(-∞, 3/2] and [3,∞)
the function f is defined by f(x) = x/x+2. what points (x,y) on the graph of f have the property that the line tangent to f at (x,y) has slope 1.2
(0,0) and (-4,2)
what are the coordinates of the POI on the graph y=(x+1)arctanx
(1, π/2)
the MVT guarantees the existence of a special point on the graph of y=√x between (0,0) and (4,2). What are the coordinates of this point?
(1,1)
the point on the curve 2y=x^2 nearest to (4,1) is
(2,2)
the graph of y=5x^4-x^5 has a point of inflection at
(3, 162) only
the radius of a circle is decreasing at a constant rate of 0.1 cm/sec. In terms of the circumference C, what is the rate of change of the area of the circle?
-0.1C
if f(x)=(x^2+1)^(2-3x), then f'(1)
-1/2ln(8e)
if f(x) = cos^3(4x), the f'(x) =
-12 cos^2(4x)sin(4x)
the graph of the function f is shown above. for which of the following values of c does lim x->2 f(x) = 1?
-2 and 0 only
if cos(xy) = y-1, then the value of dy/dx when x = π/2 and y=1 is
-2/2+π
If f(x) = ln(x+4+e^-3x), then f'(0) is
-2/5
lim x->1 x^2-1/sin(πx) is
-2/π
what is the slope of the line tangent to the graph of y=e^-x/x+1 at x=1
-3/4e
if h(x)=f^2(x)-g^2(x), f'(x)=-g(x), and g'(x)=f(x), then h'(x) =
-4f(x)g(x)
if x^2y-3x=y^303, then at the point (-1,2) dy/dx =
-7/11
given the function defined by f(x) = 3x^5 - 20x^3, find all values of for which the grpah of f is conxave up
-√2 < x < 0 or x>√2
lim as h->0 e^(-1-h) - e^-1/h is
0
the derivative of f(x)=x^4/3 - x^5/5 attains its max value at x=
1
lim as h->0 sin(π/3+h)-sin(π/3)/h is
1/2
the point on the curve x^2+2y=0 that is nearest the point (0, -1/2) occurs where y is
1/2
lim ln(4+h)-ln4/h is
1/3
when the area in square units of an expanding circle is increasing twice as fast as its radius in linear units, the radius is
1/4
let f(x) = (2x+1)^3 and let g be the inverse of f. given that f(0)=1, what is the value of g'(1)?
1/6
∫(x^3+1)^2 dx =
1/7 x^7 + 1/2x^4 + x + C
if f(x) = (lnx)^2, then f''(√e) =
1/e
in the triangle shown above, if theta increases at a constant rate of 3 rad/min, at what rate is x increasing in units per minute when x = 3 units?
12
the function f is continuous on the closed interval [2,13] and has values as shown in the table above. using the intervals [2,3], [3,5], [5,8], [8,13], what is the approximation of f(x) dx obtained from a left riemann sum
14
if log base a (2^a) = a/4, then a =
16
If f(x)=(x-1)^3/2 + (e^x-2)/2, then f'(2)=
2
lim x->0 2x^6+6x^3/4x^5+3x^3 is
2
the function f given by f(x) = 2x^3 -3x^2-12x has a relative minimum at x=
2
the radius of a circle is increasing. at a certain instant, the rate of increase in teh area of the circle is numerically equal to twice the rate of increase in its circumfrence. what is the radius of the circle at that instant?
2
a person whose height is 6 ft is walking away from the base of a streetlight along a straight path at a rate of 4 ft/s. if the height of teh streetlght is 15 ft, what is the rate at whcih the person's shadow is lengthening
2.667 ft/s
a cup has the shape of a right circular cone. the height of the cup is 12cm and the radius of the opening is 3cm. water is poured into the cup at a constant rate of 2cm^3/sec. what is the rate at whcih the water level is rising wehn the depth of the water in the cup is 5cm?
2/9π cm/sec
the slope of the line tangent to the graph of y=ln(x^2) at x=e^2 is
2/e^2
d/dx (arcsin2x)=
2/√1-4x^2
the line y=5 is a horizontal asymptote to the graph of which of the following functions?
20x^2-x/1+4x^2
if f(x) =x^2-4 and g is differentiable function of x, what is the derivative of f(g(x))
2g(x)g'(x)
if y^2-2x^2y=8, then dy/dx =
2xy/y-x^2
the function f is defined above. for what value of k, if any, is f continuous at x=2?
3
what is the slope of the line tangent to the graph of y=x^2-2/x^2+1 when x=1
3/2
the slope of the line tanget to the curve y^2+(xy+1)^3=0 at (2,-1) is
3/4
the radius r of a sphere is increasing at the uniform rate of 0.3 inches per second. at the instant the surface area S becomes 100π in^2, what is the rate of increase, in cubic inches per second, in the volume V?
30π
if ∫ f(x) dx = 6 and √f(x) dx=4, then ∫(3+2f(x))dx =
35
for what value of k will x+k/x have a relative max at x=-2
4
for the function f.f'(x) = 2x+1 and f(1) = 4. what is the approximation for f(1.2) found by using the line tangent to the graph of f at x=1
4.6
the table above gives values of the differentiable functions f and g and their derivatives at x=1. if h(x) = (2f(x)+3)(1+g(x)), then h'(1) =
44
let h be a differentiable function and let f be the function defined by f(x) = h(x^2-3). which of the following is equal to f'(2).
4h'(1)
let f be the function defined above. for what value of k is f continuous at x=2?
5
if y=(x^3-cosx)^5, then y' =
5(x^3-cosx)^4 * (3x^2+sinx)
if y= sin^-1(5x), then dy/dx
5/√1-25x^2
if y= (x/x+1)^5, then dy/dx=
5x^4/(x+1)^4
if f(x) = √x^2-4 and g(x) = 3x-2, then the derivative f(g(x)) at x=3 is
7/√5
if f(x) = 7x-3 + ln x, then f'(1) =
8
if y is a function of x such that y' > 0 for all x and y'' < 0 for all x, which of the following could be part of the graph of y = f(x)?
B
let f be the function given by f(x) = 300x-x^3. on which of the following intervals is the function f increasing?
[-10, 10]
the graph of f', the derivative of the function f is shown above. on which of the intervals is f decreasing.
[0,2] and [4,6]
the function f is given by f(x) = ax^2+12/x^2+b. the figure above shows a portion of the graph of f. which of the following could be the values of the constant a and b?
a=3, b=-4
if sin x = e^y, 0 <x<π, what is dy/dx in terms of x
cot x
lim h-> 0 e^(2+h)-e^2/h =
e^2
at x=0, which of the following is true of the function f defined by f(x) = x^2+e^-2x?
f is decreasing
If f and g are twice differentiable and if h(x) = f(g(x)), then h''(x) =
f''(g(x))[g'(x)]^2 + f'(g(x))g''(x)
let f be a continuous function on the closed interval [-3,6]. If f(-3)=-1 and f(6)=3, then the IVT guarentees that
f(c)=1 for at least one c between -3 and 6
if d/dx (f(x))=g(x) and d/dx (g(x)) = f(x^2), then d^2/dx^2(f(x^3))=
f(x^6)
The functions f and g are differentiable and f(g(x)) = x for all x. If f(3)=8 and f'(3)=9, what are the values of g(8) and g'(8)
g(8) = 3 g'(8)=1/9
if f'(x) = (x-2)(x-3)^2(x-4)^3, then f has which of the following relative extrema
i only
the graph of the function f is shown above, which of the statements if alse
lim x->4 exists
if y=e^nx, then dny/dxn
n^ne^x
If f(x) = { ln x, 0<x<=2 x^2ln2, 2<x<=4 then lim x->2 f(x) is
nonexistent
the figure above shows the graph of f' on the open interval -7<x<7. if f' has four zeros of -7<x<7, how many relative maxima does f have on -7<x<7
one
if y= x sinx, then dy/dx
sinx+xcosx
The graph of f', the derivative of the function f, is shown above. the domain is open interval 0<x<d. which of the following statements is true
the graph of f has a POI at (b, f(b))
if f is a continuous function on the closed interval [a,b], which of the following must be true?
there is a number c in the closed interval [a,b] such that f(x) >= f(x) for all x in [a,b]
an equation for a tangent to the graph of y=arcsin x/2 at the origin is
x-y=0
let f be the function given by f(x) = x^3 -6x^2. the graph of f is concave up when
x>2
what are the equations of he horizontal asymptotes of the graph of y=2x/√x^2-1?
y=-2 and y=2
which of hte following is an equation of a curve that intersects at right angles every curve of the family y= 1/x+k (where k takes all real values)?
y=1/3x^3
let f be the function given by f(x) =(2x-1)^5 (x+1). which of the following is an equation for the line tangent ot the graph of f at the point where x =1
y=21x-19
a curve has slope 2x+sinx at each point (x,y) on the curve. which of the following is an equation for this curve if it passes through the point (0,2)?
y=x^2-cosx+3