A particle moves along the x-axis so that at time t≥ 0 its position is given by x(t) = t³ + 9t² − 48t. Determine all values of t when the particle is at rest.

Q: Exercise 11 = (ƒ(x) + 5.x²)4 Let y = The Chain Rule and suppose that f(-1) = -4 and dy = 3 when…

A:

Q: DDD

A:

Q: A quadratic function fis given. f(x) = x² + 6x (a) Express fin standard form. f(x) = x (x + 6) (b)…

A: GivenQuadratic function f(x)=x2+6x We need to finda. Standard form of fb. Vertex of f, x intercepts…

Q: If √ (2-4) (2 + 6) dr = Adr 2-4 Bdr +6' then A+B =

A:

Q: Evaluate the limit of the function f defined by f(x, y) = y = x² as (x, y) approaches (0,0). x+y 2x²…

A: To evaluate the limit of the given function

Q: To which of the following will lim x+1 lim x-1X+4 x+1 lim x-1X+3 x+1 lim *4-1X+2 x+1 (x + 1)²…

A: Given, limx→ -1x+12x+22-1

Q: PROBLEM - Standard form x+5x11 =y Vertex form Axis of symmetry Opening (upward or downward) Type of…

A: Vertex form of the prabola : y =ax-h2+k ; where (h,k) is the vertex of the parabola .

Q: Let f be continuous and twice differentiable function such that f is increasing and concave down and…

A:

Q: 28. tan(x + y) + sec(x - y) = 2, (π/8, π/8)

A:

Q: 25 (6x + 5)³ But Do NOT use the Quotient Rule. a) Let f(x) = = f'(x) = Find f'(x). b) Let g(x) = 6…

A: We have to find the firstd erivative of the given functions.Recall some basic formulas: ddxxn=nxn-1…

Q: Use logarithmic differentiation to find the derivative of th y = (In(x)) cos(2x) y'(x) = ||

A:

Q: Find all of the following for the function y = x¹ ex a. x-intercept(s) b. y-intercept(s) C.…

A:

Q: A quadratic function fis given. f(x) = x² - 4x + 5 (a) Express fin standard form. f(x) = x² + 1 (b)…

A:

Q: Assume that I and M are real numbers such that lim_f(x) = L and lim_g(x) = M. Let c be x→a x→a a…

A:

Q: dt x(t) + 9 at dt 3x x(0)=8 x(0) = 9 x" (0)=12 then find x(0.25) a. (3 decimal P

A: we will find the required.

Q: Due to unavoidable wear and tear, the output from an aging packaging machine is expected to decrease…

A: current output of the machine = 8525 unit per hour

Q: Consider the following infinite series. Complete parts (a) through (c). 80 2 Σ k=1 3K-1 a. Find the…

A:

Q: Find the equation of the tangent line to the function f(x) = 2x² - x at the point where X x = -1.…

A: Given query is to find the equation of the tangent line.

Q: and all functions that have a derivative functions have the form 0

A: Topic:- application of integration

Q: Find y" by implicit differentiation. 2x² + y² = 9 y" = x

A:

Q: exfex=6x²8h

A:

Q: An initial investment of $30,000 is made in an account where interest is compounded continuously. If…

A: An initial investment of $30,000 is made in an account where interest is compounded continuously. If…

Q: Homework: four companies locations V,X,Y and Z are given with rating with respect to certain factors…

A:

Q: The graph of a function is shown below. Over what interval(s) of x is the function decreasing? V

A: Given query is is to find the interval where function is decreasing.

Q: Exercise 3 Determine the derivative to a function applying a combination of sum, difference and…

A:

Q: Find dz dt · at (x, y) = (−2, −1) for z² = x² + y² if de = dt = help (numbers) 10, dt 5, and x > 0.

A:

Q: H.W: Solve the following equations.. ............. der. 2 X y Xay. y.³). dx.

A:

Q: Please show your answer to at least 4 decimal places. 4x Determine the gradient of f(x, y) = e¹*…

A: I am attaching image so that you understand each and every step.

Q: Find the derivative y'(x) implicitly for the equation y' (x)= 3y-2y 3x+7+3y 3x+7 = 2x+jr²³.

A:

Q: Determine the area of the region bounded by two the curves f(x) = 2²-26z+72 and g(x)= 13z +36.

A: To find the area of the region bounded by the two curves.

Q: BOTTOM LINE QUESTION Find the exact area under the curve f(x)=x²e* from x=0 to x=2. Show your work…

A: I am attaching image so that you understand each and every step.

Q: Between 2000 and 2010, the use of opioids was exploding in the USA. We use MME (Morphine Milligram…

A:

Q: Suppose a product's revenue function is given by R(q) = is units sold. Find a numeric value for the…

A: Given query is to find marginal revenue.

Q: Find the derivative y'(x) implicitly for the equation y' (x)= 9x+8 V = 2x + 1³.

A: The given equation 9x+8y=2x+y3 We have to find the derivative using implicit derivative.

Q: A particle moves along the x-axis so that its position at time 0 < t < 18 is given by x(t), whose…

A: Here position of particle represents by xt Then x't is velocity/speed of particle  so particle speed…

Q: determine the values of r for which  erx  satisfies the differential equation, we substitute  f(x)…

A: To determine the values of r for which the given function is a solution of the differential…

Q: b) f(x) = x³ x², [-1,3]

A:

Q: Differentiate. y' = || Y = 7-tan(x) y X

A:

Q: An alternative to the body mass index (BMI) for estimating the health risks of obesity is A Body…

A:

Q: 3.) Find y(4) if y=3x³ +2x² −x+9

A: Topic = Derivative

Q: If f(t) is the number of people that come into an ice cream shop on a hot day, as function of time…

A:

Q: 5. Use Lagrange multipliers to find the extreme values of the f (x, y) = x² + 2y² subject to the…

A: By using Lagrange multipliers to find the extreme values of the function fx, y=x2+2y2 subject to the…

Q: Y = -3° +10 the graph can be obtained from =3x,

A:

Q: region

A:

Q: Find the absolute maximum and absolute minimum of the function f(x) = 3 sin (x) cos (x) over the…

A: We will find the required.

Q: Show that for integers a, n satisfying 0 < a <n, ged(a, n) = gcd(n, n-a)

A: Solution is given below:

Q: use the appropriate compound interest to find the amount after 4 4 years the account. io 21,000…

A:

Q: From what rule of differentiation does the Integration by Parts formula come? For each of the…

A:

Q: Let Y represent the profit (or loss) for a certain company X years after 1975. Based on the data…

A: We have given model Y=-0.68X+21.75 To get profit in 1993 Put, X=1993-1975 =18 So, Y=-0.68×18+21.75…

Q: 7. Let f(x, y) = 2, where x = 2 cos u and y = 3 sin v. Find fu(x, y) and f(x, y) and y exprees them…

A: