Find intervals on which the function is: (a) increasing (b) decreasing (c) concave up (d) concave down find any (e) local extreme values and (f) inflection points for the equation y = x to the 4/5 power times(2-x)
Let f be the function defined by f(x)=sin squared x - sinx for 0<or=x<or=(3pi)over 2. a. find the x- intercepts of the graph of f b.find the intervals on which f is increasing c. find the absolute maximum and absolute minimum value of f. Justify your answer.
The parabola y = (x^2) + 3 has two tangents which pass through the point (0, -2). One is tangent to the to the parabola at (A, A^2 + 3) and the other at (-A, A^2 + 3). Find (the positive number) ? If a ball is thrown vertically upward from the roof of 64ft foot building with a velocity of 96 ft/sec, its height after t seconds
Find the derivative of: f(x) = sqaure roo 4 / t^3 f(x) = 5 + 2/x + 4/x^2 f(x) = ((4x^3) - 2)/ x^4
Let g(x) = 300-8x^3-x^4 -Find the local maximum and minimum values. -Find the intervals of concavity and the inflection points. -Use this information to carefully sketch the graph of g.
Find dy/dx by implicit differentiation of the following: x^4-y^4-x+y=10 x^3y^3-x^2y^2+y=19 Any help would be appreciated! Thank you
Ichiro hits the ball and runs toward first base with a speed of 25 feet per second. The shortstop, who is exactly 40 feet in from third base on the baseline, gets the ball exactly 1.7 seconds after Ichiro started running (assume he runs at a constant rate.) At what rate is Ichiro's distance to the shortstop increasing at the m
A series of swells passes through a group of surfers. They notice that for a few minutes, the waves pass through at regular intervals: every 14 seconds. Let t=0 be the time when the wave is at its lowest point. The maximum instantaneous increase in height of the wave is 2.25 feet per second. a. Find r(t), the rate of chang
Find the sum: 1/8+1/4+1/2+1+........64
A highway patrol helicopter hovers 3/10 mile above a level, straight interstate highway which has a posted speed limit of 65 miles per hour. The helicopter pilot sees a car on the highway and determines with radar that at that particular instant, the distance between the helicopter and the car is 1/2 mile and is increasing at a
What is the square root of the ln of x?
What are Gerhard Gentzen's mathematical accomplishments?
Prove that the point p is a limit point of the point set X if and only if each open point set containing p contains a point in X which is different from p. Prove without using sequences. Only use the def. of open set, open interval, and that the point p is a limit point of the point set X means that each open interval containing
A rectangular lot, 54 square yds. in area with a perimeter fence, is divided into 2 rectangular sections by a single connecting fence costing $2.00/yd. the perimeter fence costs $5.00/yd. Find the dimensions of the lot which minimizes the cost of fencing.
A movie theater has a screen that is positioned 10 feet off the floor and is 25 feet high. The first row of seats is placed 9 feet from the screen and the rows are 3 feet apart. The floor of the seating area is inclined at an angle above the horizontal and the distance up the incline that you sit is x. The theater has 21 ro
1) The area of a circle is decreasing at the rate of 2 pie cm^2/s. At what rate is the radius of the circle decreasing when its area is 75 pie cm^2? 2)Find f'(-1), given f(y)=h(g(y)), h(2)=55, g(-1)=2, h'(2)=-1, and g'(-1)=7
Solve (1-x^2)^(1/2)y'+1+y^2=0 xy(1+x^2)y'-(1+y^2)=0 xyy'=1+x^2+y^2+x^2y^2 sinx(e^y + 1)dx=e^y(1+cosx)dy, Y(0)=0
A model rocket is fired vertically upward from rest. It's acceleration for the first three seconds is a(t)=60t at which time the fuel is exhausted and it becomes a free falling body. After 17 seconds, the rocket's parachute opens and the velocity slows linearly to -18 ft/sec in 5 seconds. The rocket then floats to the ground
At 2:00 pm a car's speedometer reads 30 mi/h. At 2:10 pm it reads 50 mi/h. Use the mean value theorem to show that at some time between 2:00 and 2:10 the acceleration is exactly 120 mi/h^2. Please show line by line work and be as clear as possible.
If the tuition at a certain college is determined to cost $ 32000 in 10 years, how large must a trust fund that pays 7.5% compounded continuously be, in order for a child on her 8th birthday to ensure sufficient funds at age 18?
I have two problems (well, one problem with three parts and another one): 1. (a) Let f(x)=ax^2+bx+c, a does not equal zero, be a quadratic polynomial. How many points of inflection does the graph of f have? (b)Let f(x)=ax^3+bx^2+cx+d, a does not equal zero, be a cubic polynomial. How many points of inflection does the grap
A robot is guided towards an object by a software algorithm that controls its position such that the path of the robot is approximately sinusoidal, with a period 2, as shown in Figure B4 (attached). (a) Show that the length l of any single-variable function f(x), between the limits of x=a and b, can be expressed by th
Suppose m and k are positive numbers. Find u so that mu''(t) + ku(t)= 0 for all numbers t and u(0)=1 and u'(0)=2. (note: u'' = second derivative of u) Please clarify any shorthand that you are using. Thanks!
A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible volume of such a cylinder.
Show that the equation 3x - 2 + cos(pi x / 2) = 0 has exactly one root. (This problem may be clearer in the attached file.)
The curve 2(x^2 + y^2)^2 = 25(x^2 - y^2) is called a Lemniscates. Find the tangent line at (3,1). (The problem is also attached in MS Word with the appropriate fonts)
Given the ellipse x2/4 + y2/9 = 1 What are the points where the tangent line is vertical? (In narrative, the problem reads: given the ellipse x squared divided by 4, plus y squared divided by 9, equals 1, what are the points where the tangent line is vertical? The problem is also attached in MS Word, in case you need it
Solve for t. lim t-->0 (sin t)^2 / (4t)^2
A kite 100ft above the ground moves away horizontally at a speed of 8ft/sec. At what rate is the angle between the string and the horizontal decreasing when 200ft of string has been let out?