A point moves along the curve y= 2x^2 - 1 in such a way that the y value is decreasing at the rate of 2 units per second. At what rate is x changing when x = -3/2 ?
Not really looking to solve just an explanation on the process of how to get to the solution. Thanks!!
since you said in your problem the value of the rate of y was -2, the graph of the function would be decreasing.
you could try the first derivative test to see at which intervals the function would be increasing or decreasing, but from the values you have, as x gets bigger, y gets smaller
for this and other problems with related rates, make sure you know the formulas. for a sphere
when you differentiate the function you get
you know that is 2in^2/sec, volume with respect to time. radius is 1, just solve for dr/dt, the rate of change of the radius with respect to time. with these problems, its just taking your derivative, realize what is changing and plug in what you know
make sure you use the thank button
A maximization problem. A square is to be cut from each corner of a piece of paper which is 8 cm by 10 cm, and the sides are to be folded up to create an open box. What should the side of the square be for maximum volume? What's the basic process for maximizing problems?
find a way to relate length width and height...if u draw a picture you will see that the length is 10-x and the width is 8-x for the base of the box. the height is simply x, so V=(10-x)(8-x)(x). you can multiply, then differentiate the function. you set it equal to zero and you will get values for x. you must use the 1st or sometimes 2nd derivative test to see whether the values you got are maximums or minimums.