6. Given the function f(x)= x² find the equation of g(x) where f(x) is shifted to the right 2 units, %3D 1 shifted down 3 units, and compressed by

Q: 1) Find the second derivative for the following functions: a) f(x) = 4x³ + 3x² + x – 14 b) f(x) =…

A: Solve derivative a fx=4x3+3x2+x-14b fx=4x-3+2x-4c fx=5ex-e3x

Q: The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their…

A: Given, Cost function, C(x)=100+39x-0.07x2

Q: Suppose x and y are functions of third variable t. In the equation x2+y2=45, what are the values of…

A: In the question it is given that x and y are the function of the variable t in the equation…

Q: 12. Given the function y=6x-2, find the derivatives O -6 O 2 O -2 Required

A: Topic:- calculus

Q: 2. Next we plotted the slopes of g(x) = x2 and h(x) = x³. What was g'(x)? What was h'(x)? h'(x)= 3x…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Suppose that the intensity of a point light source is directly proportional to the strength of the…

A:

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A: given that pressure and volume are related by the equation PV1.4=C and a certain instant of time…

Q: Two people run for 13 seconds with velocity functions vi = a m/s for person A and vz = 3/Tm/s for…

A: Topic = Algebra

Q: Suppose that a companys sales volume, y (in thousands of units) is related to its auvertising…

A:

Q: 8) A company's demand equation is x - V 2000 - p² , where p is the price in dollars. Find dp/dx when…

A:

Q: Provide the equation of the line tangent to the given function at the specified point g(x)=ln(x^2);…

A: Given : gx = lnx2

Q: 4. Write the equation of the line tangent to f(x) = (e* +2x +1)In(e* +2x+1), when x = 0.

A:

Q: We are given f(x) = 9x2 and f '(x) = 18x. Find the instantaneous rate of change of f(x) at x = 2.

A: Given function is

Q: The rate of growth of a population P is given by dP/dt=kP + N  where N is a constant representing…

A: Given:- The rate of growth of a population P is given by dP/dt=kP + N where N is a constant…

Q: Suppose a company wants to introduce a new machine that will produce a rate of annual savings​ (in…

A: given S'x=150-x2C'x=x2+114x where S'x is the rate of annual saving and C'x is the rate of annual…

Q: Suppose you are climbing a hill whose shape is given by the equation z = 1000 −0.005x^2 −0.01y^2…

A:

Q: Suppose that the total cost function, in dollars, for the production of x units of a product is…

A:

Q: A particular radioactive isotope has a half-life of 400 years. The time required for only A% of the…

A: The half-life of the radioactive element is the time during which half of the radioactive element…

Q: Suppose x and y are functions of third variable t. In the equation x2+y²=45, what are the values of…

A: This question is related to application of derivatives.

Q: Does the given equation define an implicit function around the point (y=3, x=1) and why?

A:

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Given functions are: y=a2-t2x=42t2+a In order to calculate d2ydx2, firstly we will calculate d2ydt2…

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A:

Q: 1) Use the definition of the derivative to find f'(x) f(x) = (4x + 1)(3 – 7x³) Step 1: Step 2: Step…

A: Topic:- function and it's Derivatives

Q: 13. In y = what is the derivative of 2x2 +3? x+1 a) 2x b) 4x c) 4x +3 d) 7

A:

Q: ズ-1 f(x)- X + 3

A:

Q: 27. The first derivative of y = is (4x+1) -24 b. 24 C. -6 6. (4x + 1)+ (4x + 1)+ (4x + 1)4 (4x + 1)*…

A: y=-2(4x+1)3

Q: Suppose that the marginal propensity to save is given by equation below and that consumption is $6…

A:

Q: A particle is moving on the x-axis and the position of the particle at time t is given by x (t),…

A:

Q: Find f'(x) and find the equation of the line tangent to the graph of fat x = 1. f(x) = (2+5x)(5-4x)

A:

Q: Find the marginal profit for producing x units. ( P = -0.3x³ + 10x² – 168.45x - 3000 dP dollars per…

A: Marginal profit is the measure of the increment of the profit function for unit increment of x, at a…

Q: An object is moving along a path that can be described as f(x) meters, where x is in seconds and…

A: Topic = Application of derivative

Q: The revenue (in millions of dollars) from a manufacturing process is projected to follow the model R…

A: Profit=Revenue-Cost

Q: A company determines that its total cost, in thousands of 3x rands, for producing x items is C =…

A:

Q: 1. Suppose that the volume V of a certain cone can be expressed as V =nh, where h is the height of…

A: For the solution of the problem follow the next steps.

Q: If f and g are functions of time, and at time t = 2, f equals 2 and is rising at a rate of 3 units…

A:

Q: Match the functions in Column A with their derivatives in Column B. 1. f(x) = 4 А. f'(x) = 8x 2.…

A:

Q: Q4. Find the slope of the tangent line to the function f(x)= e* +3; x+2 at x=4 5x-10

A: Given : fx = ex5x-10

Q: Suppose we have a revenue function given by R(x)=3x^3−αx, where α is a constant. What would the…

A: Formula used:

Q: Find the level curve of the function at c=2 for g(x,y)=(x^3-y)

A: A scalar function g(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: 25. Find the derivative of the function. y = (1+ 3x)e - 3x O A. - 9e - 3x 3x В. - 3(1 + 3х)е - 3x -…

A:

Q: 4. What is the SECOND derivative of the given function? * y = 3x³ - 2x² + x - √ y" =9x² - 4x + 1 y"…

A:

Q: Suppose that the profit (in dollars) from the sale of Kisses and Kreams is given by P(x, y) = 10x +…

A: Px,y=10x+6.2y-0.008x2-0.02y2

Q: Find the value of x for which the marginal profit is zero. C (x) = 2x, R(x) = 6x – 1,000

A:

Q: 11. 5 4 Determine the derivative of y=x° – x* + 6. - Enter your next step here dy ab a + JT 00 () dx…

A:

Q: 9. The derivative of the graph x+y² D5 with respect to time is c-2y+ 20 C. a. y +x d. -y 2x +2y

A: Q 9 Given that: The graph: x2+y2=25

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A:

Q: 18. Up to what derivative is the derivative of y = x6 + 2x5 - 4x4 + 7x³ becomes 0.? a. yv b. yu c.…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.