Derivatives
Integrals
Applying Derivatives
Applying Integrals
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100
If f(x) = 3x2 - 2x5 + 2x - 765, what is f'(2)
f'(2) = 174
100
∫ 12 dx
12x + c
100
What is a critical point of the function f(x)=3x2 - 3x
(1/2,-3/4)
100
Find the area under the curve between x=0 and x=10:
The area under the curve is 5
100
If f(x)=ln(4x), what is f'(x)?
f'(x)=1/x
200
If f'(x) = ln(x) + 7x2 - 37x + 21 what is f''(5) ?
33.2 or 166/5
200
3∫cos(x)
3sin(x) + c
200
What is the x-coordinate of one local Maximum of the function shown in the graph? (Rounded to the nearest whole number)
x=-2, 4
200
A particle is moving along an axis. The velocity of a particle is modeled by the equation v(t)=3t2+7. If the particle's position on the x-axis is 3 at t=0, what is it's position at t=4?
At t=4, the particle's position is equal to 95.
200
Let the position of a particle be modeled by s(t)=s4+3t-70, what is the instantaneous velocity at t=5?
The velocity is 503.
300
If f(x) = (1/x) + 39x3 what is f''(x) ?
f''(x) = 234x + (2/x3)
300
∫4x6 - 2x3 +7x - 4 dx
(4/7)x7 - (1/2)x4 + (7/2)x2 -4x + c
300
f(x)=3+3xe2x-10 at x=5, what is the equation of the tangent line ?
y-18 = 33(x-5)
300
Write and then solve an integral to determine the area below f(x)=3+2x−x2 and above the x-axis.
A=∫3+2x−x2dx Bounds are from -1 to 3 -> area is 32/3.
300
Evaluate the limit:
0
400
if f(x) = 4 * ((3x+9)-7))1/2 what is f'(x)
(6) / (3x+2)1/2
400
∫1/(sqrt(4x-x2) dx , what is f(x)?
arcsin(x/2) + c
400
limt→∞ (ln(3t)) / t2
0
400
Determine the average value for f(x)=8x−3+5e2-x on [0,2].
(1/2)(5+5e2)
400
3/16 (B)
500
if f(x)=h(x)2 + g(3x), what does f'(x) equal?
2h(x)*h'(x) +3g'(3x)
500
∫ 3√z + 10 5√z3 dz
(3/4) w4/3+ (25/4)w8/5 + c
500
Find two positive whole numbers whose sum is 300 and whose product is a maximum...
Both numbers equal 150.
500
dy/dx = ∫x2/(1-y2) Find a solution to the differential equation (leave the constant as C).
y2-2y=x3+2x2+2x+C
500
if f(x)=sin(x)cos(x)+sec(x), what is f"(x)?
f"(x)=tan2(x)sec(x)+sec3(x)−2sin(2x), if you get an answer equal to this than you earn the points.