Integration Station
Given the interval [-2,4] the absolute maximum of f(x)=x3-3x2+12 occur f'(x)=3x2-6x
What is the value Max=(4,28)
The width of a rectangle is increasing at a rate of 2 cm/sec and its length is increasing at a rate of 3 cm/sec. At what rate is the area of the rectangle increasing when its width is 4 cm and its length is 5 cm
dA/dt= 22 cm2/sec
Air is being pumped into a special balloon so that its volume increases at a rate of 100 cm3/s. How fast is the radius increasing when the diameter is 50 cm
dr/dt=1/25 cm/s
A plane flying horizontally at an altitude of 1 mile and a speed of 500 mph passed directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 miles away from the station
250√3
Car A is traveling east at 50 mph away from an intersection. Car B is traveling north at 60 mph towards the same intersection. At what rate are the cars approaching each other when car A is 0.3 miles and car B is 0.4 miles from the intersection
-18 mph
An open-top box with a square bottom and rectangular sides have a volume of 256 cubic inches. Find the dimensions that require the minimum amount of material.
8x8x4 Cubic inches
At how many points on the curve x3/2+y2/3=9 in the xy-plane does the curve have a tangent line that is horizontal.
Two points=+-27
A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area
X=600 ft
Y=1200 ft
If A=X2 and dx/dt=3 when x=10 find dA/dt
60
An aircraft has taken off from an airstrip and is climbing at a 30 degree angle to the horizontal. How fast is the aircraft gaining altitude if its speed is 500 mph.
250 mph
Find the linearization L(x) of the function f(x)= tanx of the function at a =π/4
y=3/2(x-1)+1
A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius r of the outer ripple is increasing at a constant rate of 1 foot per second. When the radius is 4 feet, at what rate is the total area A of the distributed water changing
8π ft2/s
Find the global extrema of f(x)=1/3x3-2x2 on the interval [-1,3]
f(0)=0 Abs. Max
f(3)=-9 Abs Min
Suppose x and y are both differentiable functions of t and are related by the equation y=x2+3. Find dy/dt when x=1, given that dx/dt=2, when x=1
dy/dt=4
A rectangular storage container with an open top and a square base is to have 20ft3. Material for the base costs $5 per square foot. Material for the sides costs $2 per square foot. Find the cost of materials for the cheapest such container.
$76.10
A fire has started in a dry, open field and spreads in the form of a circle. The radius of the circle increases at a rate of 6ft/min. Find the rate at which the fire area is increasing when the radius is 1500 ft
1800π ft2/min
As a circular metal griddle is being heated, its diameter changed at a rate of 0.01 cm/min. Find the rate at which the area of one side is changing when the diameter is 30 cm
.15π cm2/min
Let f be a differentiable function such that f(3)=2 and f'(3)=5. If the tangent line to the graph of f at x=3 is used to find an approximation to a zero of f
2.6
Find the linearization L(x) of the function at A
f(x)=x-2x2
A=5
Y=19(x-5)-45
Find the extrema values of 2x3-15x2+24x=7 on [0,6]
(0,7)
(1,18) Rel Max
(4,-9) Abs Min
(6,43) Abs Max
Find the linear approximation for h(x)= 3√8-x at a=0 and use it to estimate 3√7.96
599/300
The radius of a circle is increasing at a rate of 2 centimeters per minute. Find the rate of change of the area when (a) r=6 centimeters and (b) r=24 centimeters
24π cm2/min
96π cm2/min
If v=-5p3/2 and dv/dt=-4 When v=-40 find dP/dt
4/15
Consider the curve x2-3=ey in the xy-plane. At the point (-2,0) is the curve concave up or concave down
concave down
Two numbers whose sum is 80 and whose product is a maximum
What is x=40 and y=40
The function f is twice differentiable with f(2)=1 f(2)=4 and f''(2)=3. What is the value of the approximation of f(1.9) using the line tangent to the graph of f at x=2
.6
A carpenter is building a rectangular room with a fixed perimeter of 54ft. What are the dimensions of the largest (max area) room that can be built.
Dimensions= 27/2ft x 27/2 ft
All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume changing when each edge is (a) 1 centimeter and (b) 10 centimeters
9 cm3/sec
900 cm3/sec
If p= 3/w and dp/dt=5 when p=9 find dw/dt
-5/27
f(x)=x2-6x Find when increasing and decreasing
decreasing (-∞ ,3)
increasing (3,∞ )