The number of miligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by x(t)= 2000t/t^2+16 (a) For what t-values is x increasing? (b) Find the t-value at which s is maximum. (c) Fine the maximum value of x.
The number of miligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by
x(t)= 2000t/t^2+16
(a) For what t-values is x increasing?
(b) Find the t-value at which s is maximum.
(c) Fine the maximum value of x.
Expert Answer
Want to see the step-by-step answer?
Derivative
Related Calculus Q&A
Q: During the first four months of employment, the monthly sales S (in thousands of dollars) for a new ...
A: Part (a)S= S(x)= 9 / x + 10 + x / 4, x ≥ 4The given function is defined only for x ≥ 4. We don't hav...
Q: Please sketch this by hand! And show all your steps as im doing my best to fully understand the proc...
A: (A) The function has an absolute maximum but no local maximum. This means the graph is strictly incr...
Q: How can I get the result? Which is the result?
A: The given function is,
Q: find the derivative of g(x)= 3x3- 2/ square root x you dont need to simplify answer, but use paren...
A: The given function is,
Q: If l0g x=0.35 and fog6N0.5, evaluate the fo llowig expression.
A: Here, we use the above log rules.
Q: If y (x25x-1)e2x then y (3x2-10x+7)e2x O (2.7x+4)e2x O(22+ 12x + 3)e2x (2x+5)32x (2x 52-1
A: Given,
Q: Determine the location and value of the absolute extreme values of f on the given interval, if they ...
A: The function is defined as
Q: 3x4 y‴+9x4 =5xy′+5x5 y″+9lnx Determine the order of the differential equation shown above.
A: The given differential equation is,
Q: y′=3x−2 Find the particular solution to the equation shown above that passes through the point (−10,...
A: Firstly, we separate the variables x and y, and then integrate both sides.
Q: Let R be the region bounded by y x, x 1, and y 0. Use the shell method to find the volume of the sol...
A: (A)It is given that, the region bounded by y = x2, x = 1 and y = 0.The region around the line y = -8...
Q: Marginal Revenue. Suppose the total revenue function for a blender is R(x)= 36x-0.01x2 dollars where...
A: The total revenue function for a blender is R(x)= 36x-0.01x2 dollars where x is the number of units ...
Q: The area of a circle increases at a rate of 3 cm^2 per second. Find a) how fast is the radius changi...
A: Given information:The area of a circle increases at a rate of 3 cm square per second
Q: Logarithmic differentiation
A: The given function is y=(x+1)²(x-2)(x²+3).
Q: find the exact length of the curve of the equation below, show all work y = ln(sec(x)), with a range...
A: First, we find the dy/dx
Q: How does the limiting behavior of solutions depend on the value of y(0)?
A: Given autonomus differential equation:Graph of function f is given.We need to show the the limiting ...
Q: Find y' if x^y = y^x .
A: Given,
Q: A hot-air balloon is 190 ftabove the ground when a motorcycle (traveling in a straight line on a h...
A: Let x be the horizontal distance from balloon to motorcycle, y be the vertical distance from the bal...
Q: find the inverse of y from the function that is in the picture below
A: Giveninformation:The given function is
Q: Help with #8
A: Let's understand the formula for calculation of curvature.For a function, y(x) the curvature is give...
Q: Use Newton's method to approximate all intersection points of the following pair of curves. Round to...
A: Before we get into the solution of the question, let's understand a bit about Newton's method. If xn...
Q: Use any method to determine if the series converges or diverges. Give reasons for your answer.
A: The given series is
Q: approximate the area under the graph of f(x) and above the x-axis using the following methods with n...
A: Given:The function is f(x) = ex-1.The interval (a, b) is (0,1)
Q: lim x→5 f(x) where f(x)= { 7x-10 if x<5; 25 if x>=5
A: To find the limit x->5 f(x), we have to find the right and left limit of x=5 first.
Q: 2. Given the given function f(x) = x+defined on the interval [1, 3], determine if the function satis...
A: The given function is continuous and differentiable on the whole real numbers except zero. In partic...
Q: Find the position and velocity of an object moving along a straight line with the given acceleratio...
A: Obtain the velocity as follows.
Q: k 5k! x Find the radius of convergence of- (2kk The radius of convergence is Type an exact answer in...
A: We have to find radius of convergence of series.Series is given below:
Q: How can I get the result? Which is the result?
A: (a)we are given a function
Q: a. Determine whether the Mean Value Theorem applies to the function f(x)= ex on the given interval [...
A: Definition used: Mean Value Theorem
Q: Determine the radius and interval of convergence of the following power series. к?(- 5)2к k! The rad...
A: Given,
Q: Find the slope of the tangent line to the given polar curve: r = 2 - sin(theta), at theta = (pi/3) s...
A: Click to see the answer
Q: How do I solve the initial value problem using P(x), Q(x) and v(x)?
A: First we find P(t) and Q(t) by comparing with y\'+P(t)y=Q(t).
Q: 1000 Find the marginal cost when q = 10. 9 The average coste for producing q units of a product is g...
A: The average cost c is given by ,
Q: a. find a possible function f and number a b. evaluate the limit by computing f`(a).
A: We first write the given function in the form of the definition of the derivative.
Q: Help me please..
A: The Taylor series for cosx at x=0.
Q: Help with #4
A: Click to see the answer
Q: 18. CCT 11 The quantity (in pounds) of a gourmet ground coffee that is sold by a coffee company at a...
A: The quantity (in pounds) of a gourmet ground coffee sold at the price of p dollars per pound is give...
Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is inf...
A: We first have to factor the numerator and the denominator.
Q: (2x-3)4 dx 10
A: Given:The integral is
Q: :)
A: Given:The given curves are y = x2, x = 1, and y = 0.The volume of the solid revolved around the line...
Q: How can I get the result? Which is the result?
A: Click to see the answer
Q: Which of the following is the power series representation for g(x)? +8 OA. B. k 8 1 k 0 k 0 8k O C. ...
A: Note that the function g(x) is not provided (here option (c) can also be a power series). So, we are...
Q: The rectangular coordinates of a point are given. Find polar coordinates of the point. Express 0 in ...
A: Let the polar coordinates of given point are ( rcos(thita), rsin(thita)) as shown on board.By compar...
Q: x1 J: (x2+2x)2 dx= (x2+2x)3 C (x2 2x)3 C + 3 (x2+2x)3 +C 6 22-1C + -2 2x)1+C
A: Click to see the answer
Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function x2 In(1 x...
A: We know the Maclaurin series for ln(1+x). From there we find Maclaurin series for ln(1+x^3) by repla...
Q: find the derivative of the question in the picture please show all work
A: Obtain the derivative of the function.
Q: Water drains from the conical tank at the rate of 5ftmin 14. 4 10 Exit rate: 5 ft/min a. What is the...
A: By using the concept that the sides of similar triangles are proportional, therefore, the ratio of r...
Q: The funciton f in the figure satisfies the lim f(x)=5 as x approaches 4. Determine the maximum valu...
A: (A) From the inequality |f(x)-5|<1 , we\'ll find range of f(x) first.
Q: Evaluate the following integrals (a) x^5dx (b)(5^2+x^10)dx (c) (12x^5+12x^3-7)dx (d) (x^3-7-(3/x^4))...
A: You have asked a question with multiple sub parts. I will address the first three of them. Please po...
Q: Use a reference triangle in an appropriate quadrant to find the given angle.
A: The given equation is,
Q: 3x2-3 and y(0) = 8, then y(1) = If dx 4. 12. 0. 8 6.
A: As a first step, let\'s rearrange the term. Please see the white board.