Theme: Derivatives...
  • if 10 800 cm2 of material is available to make a box with a square base and an open top find the largest possible volume of the box.
  • Determine whether there is a maximum or minimum vale for the given function, and find that value. f(x)= x^2+6x+4
  • If a function f is continuous for all x and if f has a relative maximum at (-1, 4) and a relative minimum at (3,2), which of the following statements must be true? (a) The graph of f has a point of inflection somewhere between x = -1 and x= 3 (b) f’(-1) = 0 (c) this is wrong (d) The graph of f has a horizontal tangent line at x = 3 (e) The graph of f intersects both axes - Correct answer I understand why e is correct, but I do not get why a, b, and d are all wrong. Aren’t b and d to be expected since they are relative max/min’s? I also can’t imagine a case in which "a" is incorrect. Can someone explain why they are wrong? Thank you!
  • Simple question Derivative of \( \boxed{f(y)= \frac{y^2}{y^3+8} } \)
  • Find the second derivative for y=(x+2)/(x-3)
  • Find the derivative of the function. y=sqrt( 3x+sqrt( 3x+sqrt( 3x)
  • Not sure how to do #69, it’s a calc 1 question
  • What is the derivative of y=e−1y=e^(-1)?
  • What is the derivative of y=3tan(x)y=3 tan (x)?
  • find the derivative of y=tan(arcsin(x)y=tan(arcsin(x)?
  • find the derivative of y=arcsin(2x+1)y=arcsin(2x+1)?
  • The profit function for a business is given by the equation P(x)=−4x2+16x−7, where x is the number of items sold, in thousands, and P(x) is the profit in thousands of dollars. Calculate the maximum profit and the number of items that must be sold to achieve it.
  • Find all points on the curve xy^2-3x^2y=10 whose x-coordinate is 1, and write the equation for the tangent line at each of those points
  • A potter forms a piece of clay into a cylinder. as he rolls it, the length L, of the cylinder increases and the radius, r, decreases. If the length of the cylinder is increasing by 0.4 cm per second, find the rate at which the radius is increasing when the radius is 2 cm and the length is 6 cm.
  • 1. A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box that minimize the amount of material used. 2. A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $20 per square meter. Material for the sides costs $12 per square meter. Find the cost of materials for the cheapest such container.
  • Ex 2.8 3. find the maximum value of y for the curve y=x^5 -3 for -2≤x≤1
  • Two ants are at a common point at time t=0, the first ant starts crawling along a straight line at the rate of 4 ft/min. Two minutes later, the second ant starts crawling in a direction perpendicular to that of the first, at a rate of 5 ft/min. How fast is the distance between them changing when the first insect has traveled 12 feet? !
  • What is the derivative of x to the minus 5 power
  • How to find the derivative 5x²-2x+1
  • The graph below is the graph of the DERIVATIVE of a function f. Use this graph to answer the following guestlons about f on the interval (0,10). In each case be sure to justify your answer. A. On what subinterval(s) is f increasing? B. On what subinterval(s) is f decreasing? C. Find the x-coordinates of all relative minima of f. D. Find the x-coordinates of all relative maxima of f. E. On what subinterval(s) is f concave up? F. On what subinterval(s) Is f concave down? G. Find the x-coordinate of ail points of inflection of f. H. Make a sketch of f.
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