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A hamburger wrapper is thrown from a third floor dorm window, and its motion can be modeled by the equation h(t) = -3t^2 + 6t + 30, where h is the height in feet and t is the time in seconds.
a. Find the vertex of the parabola, then describe what it tells us physically about the situation.
b. Find the x-intercept, then describe what it tells us physically about the situation.
Suppose f(x)={kx + 7 ; x>= 2 ,x^2+19 ; x < 2' , For what value of k is lim x→2 f(x) defined?
Q. Write down 10 uses of Surface Integration in computer science Engineering
For the following functions:
(a) f(x)=(x+2)²(x-1)
(b) f(x)= (x²)/(x²-9)
(c) f(x)= (x²-2x+1)/(x+1)
i. Find the critical numbers off (if any);
ii.Find the open interval(s) on which the function. increasing or decreasing
iii. Apply the first derivative test to identify all relative extrema;
iv. Use graphing utility to confirm your results.
Consider the function f(x)=sin x cos x+5 on the interval (0, 2pi).
(a) find the open interval(s) on which the function increasing or decreasing, and
(b) apply the first derivative test to identify the relative extrema.
Determine the open intervals on which the graph of f(x)= (x²)/(x²+1) is concave upward or concave downward
Find the points of inflection and discuss the concavity of the graph of the function
f(x)= (x+1)/√x
Find all relative extrema. Use the second derivative test where applicable.
(a) f(x)=√x2+1
(b) f(x)=cos x -x
Pebbles are poured out of a tube at one cubic meter per second. It forms a pile which has the shape of a cone. The height of the cone is equal to the radius of circular base. How fast is the pile of pebbles rising when it is 2 meters high
A car manufacturing company was able to release 1,860 units at the end of January. Based on records, they were able to increase their sales by 46 units per month thereafter. In what month did their car sales reach 2, 320 units?
