If f(x) = 2 + |x-3| for all x, then the value of the derivative f’(x) at x = 3 is
-1
0
1
2
Non-existent
There is no maximum value for v
2x
1
2
-tan x
-cot x
Cot x
Tan x
Csc x
½ tan2x+C
Sec2x+C
ln |sec x| +C
ln |cos x| +C
Secxtanx+C
If a function is continuous for all x and if f has a relative maximum at (-1, 4) and a relative minimum at (3, -2) which of the following statements must be true?
The graph of f has a point of inflection somewhere between x = -1 and x =3
f’(-1)=0
The graph of f has a horizontal asymptote
The graph of f has a horizontal tangent line at x = 3
The graph of f intersects both the axes.
If f’(x) =-f(x) and f(1) =1then f(x) =
½ e-2x+2
e-x-1
e1-x
e-x
-ex
Which of the following is an equation of the curve that intersect at right angles every curve of the family y=1/x +k (where k takes all the real values)?
y=-x
y=-x2
y=lnx
2
2.03
2.096
2.12
2.24
If y = tan u, u = v – 1/v and v = lnx, what is the value of dy/dx at x= e?
0
1/e
1
2/e
Sec2e
0 and 8
8 and 16
16 and 24
24 and 32
32 and 40
2sinx+2xcosx+C
x2sinx+C
2xcosx-x2sinx+C
4cosx- 2xsinx+C
( 2 – x2)cosx – 4 sinx+C
3x2 – 3 + C
4x4 – 6x2 + C
The number of bacteria in a culture is growing at a rate of 3000e2t/5 per unit of time t. At t = 0, the number of bacteria present was 7,500. Find the number present at t = 5.
1200 e2
3000e2
7500e2
7500e5
15000/7e7
e3/2
A point moves in a straight line so that its distance at time t from a fixed point of the line is 8t -3t2. What is the total distance covered by the point between t =1 and t = 2?
1
4/3
5/3
2
5
If y = enx, then dny / dxn =
nn enx
n!enx
nenx
nn ex
n!ex
5+ c
5
5 – c
c – 5
-5
If f’’(x) – f’(x) -2f’(x) = 0,f’(0)= -2 and f(0) = 2 then f(1) =
e2+e-1
1
0
e2
2e-1
If f (x) = ex , which of the following lines is an asymptote to the graph of f ?
y =0
x =0
y=x
y= -x
y =1