Puestion 28- Given function is flx)= x-mm 5742 +574 %3D Compute deivatve. Find the following u » Inteval "of inceasing deeteasing. (2) Eatreme values. (3) Interval of Concave up l down. Plot the osiginal graph- (4)
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- Check uniquness and existance for fixed point whilef(x)=2+(x^2/3)with interval [2,3]A right triangle has one vertex on the graph of y = x3, x > 0, at (x, y) another at the origin, and the third on the positive y-axis at (0, y). Express the area A of the triangle as a function of x.A right circular cone is held with its apex facing downwards and is inscribed in a sphere with fixed radius k cm within the interval 1 cm ≤ k ≤ 5 cm and the distance from the base of the cone to the center of the sphere is x cm. a. Evaluate the maximum volume of the cone by assigning k to a value within the given interval. Discuss the difference of use between the first derivative test and second derivative test to optimize the volume. b.Water is poured into the cone at a rate of 10 m3s−1. Find the rate at which the water level is rising when the depth of the water is (x + k) − 3.
- Explain the process for determining whether the function is continuous and differentiable at the identified point. The function is attached.A piece of wire 150 cm long is cut into two parts. A square is made from the first piece, and a circle of radius r is made from the second piece. Find with the help of derivative what the length of each piece should be so that the sum of the areas of these two shapes is minimum. pls answer on paper thnx :)Just before a potential traffic accident one car is traveling at 128 km/h when the driver fully applies the brakes (so that he may avoid an accident) by producing a constant deceleration of 5 m/s2. You must find the distance traveled by the car before the car comes to a full stop. Equivalently, this is the distance from the place where the driver must hit the brakes, to the place where the car will fully stop right before/ at the potential traffic accident. find correct linear function for velocity, function of time t, with some constant, C, the intercept find correct value of the constant intercept C in part (a) find correct quadratic displacement function of time t find correct time until full stop of the car, and find correct distance
- Locate the relative extremum and point of inflection. Use a graphing utility to confirm your results. (If an answer does not exist, enter DNE.)Find the absolute maximum and minimum of the following function on the interval [0,2] State both the value and the location for each extrema. Show ALL work.A 500 gallon tank is filled with gasoline containing 10 pounds of a seasonal additive. A gasoline mixture containing 0.02 pounds of additive per gallon is added to the tank at the rate of 50 gallons per minute. The gasoline solution in the tank is continuously and thoroughly mixed and drained out at the same rate of 50 gallons per minute. How many points of additive are in the tank 30 minutes into the operation.
- Use Application of Derivatives A wire of length L is to be cut into two pieces, one to form a square and the other to form an equilateral triangle. How should the wire be divided to maximize or to minimize the sum of the areas of the square and triangle?A particle of unit mass moves on a straight line under the action of a force which is a function f(v) of the velocity v of the particle, but the form of this function is not known. A motion is observed, and the distance x covered in time t is found to be connected with t by the formula x = at + bt2 + ct3 where a, b, and c have numerical values determined by observation of the motion. Find the function f(v) for the range of v covered by the experiment.A tank that contains 20 gal of water in which 3 kg of salt has been dissolved completely is to be filled by a hose with water carrying 0.25 kg/gal of salt at a rate of 4gal/min. The mixture is then stirred and the solution isbeing pumped out at the same rate. Find the function of salt in the tank at any given time.