During a month-long advertising campaign, the total sales S of a magazine is modeled by the function S(x) = 5x2 + 90x + 10,000, where x represents the number of days since the campaign began, 0 sxs 30. (a) What is the average rate of change of sales from x = 15 to x = 25 days? AS Ax sales/day = (b) What is the instantaneous rate of change S'(7) of sales when x = 7 days? S'(7) = sales/day

Q: Which function has the same derivative function f(x) as g(x) = lnx + x² – x?

A:

Q: Solve for the derivative of the function using chain rule. 9. f(x)= esinx

A: Solve for the derivative of the function using chain rule. 9. f(x)= esinx

Q: The derivative of y = 2 ln ⁡ x − ln ⁡ x 3 is

A: The given function is, y=2lnx-lnx3

Q: What is the average rate of change of the function f(x): = x² between x = -3 and x = 3?

A:

Q: How can you sometimes graph the derivative of a function when all you have is a table of the…

A: We can draw the graph of derivative of a function using the values given to us in table of of the…

Q: 2. Show a graphical method of approximating the instantaneous rate of change at x = 3 for the…

A: You must have idea about what is the basic difference between instantaneous and average rate of…

Q: Which function has the same derivative function f (x) as g(x) = lnx + x² – x?

A: we have to find derivative

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: The given function of production cost is To find average rate of change of total cost ,use formula

Q: Estimate the instantaneous rate of change of P(x)=5/x+2 at the point x=2

A:

Q: x + x dx x2

A:

Q: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = ex−12

A: Given function is y=ex-12. To find the derivative of the given function. Solution: Chain rule of…

Q: Find the derivative of y=ln[x^3(x^2-5)^3/4]

A:

Q: Find the second derivative and the points of inflection using the second derivative f(x) = ln(x) /…

A:

Q: For y=ln2x, determine the equation of a tangent line parallel to 2x-3y+1=0

A: here we find the equation of a tangent which is parallel to 2x-3y+1=0. y=mx+c slope = m.

Q: 14) Find the first derivative of f(x)= 2*2*

A: The derivative of ax is axlna. The derivative of xn is nxn-1, where n is any integer. The chain rule…

Q: Find an expression for the derivative of the exponential function y=ex using the definition of…

A: To determine the derivative of exponential function y=ex using definition of derivative.

Q: 4 1 Y(s) = 5s2

A:

Q: Estimate the instantaneous rate of change at the point x=2 for f(x)=ln(x) ROC =

A: the fiven function is f(x)=ln(x)

Q: If the instantaneous rate of change of ƒ1x2 with respect to x ispositive when x = 1, is ƒ increasing…

A: As instantaneous rate of change  of f(x) that is f'(x) is positive means the function f(x) is…

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Given,         The total cost in dollars from the production of x printers is given by…

Q: How do you find the derivative of the sum of two functionsƒ + g?

A: we have to determine how to determine the derivative of the sum of two functions that is f+g.

Q: Find the derivative: y = ln(24) 2x-4 O 4x-x² 2x-4 x²-4x 4 4x-x² 4 x²-4x O о O 8

A:

Q: The rate of change of the male population of a particular barangay is proportional to the male…

A:

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Suppose total cost in dollar from the production of x printers is given byC(x) =…

Q: The second derivative of a function is equal to 1. If the graph of the function passes through (0,2)…

A:

Q: Example 4:- By using the four steps rule, find the derivative of the function f(x) = Vx + 2

A:

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = ex−12

A:

Q: Compute the derivative: x4 – 4 d - at x = 2 dx x2 – 5 - The derivative is:

A:

Q: Five mice in a stable population of 500 are intentionally infected with a contagious disease to test…

A: We will form a differential equation and then solve it to get number of mice infected after a…

Q: State the derivative rule for the exponential function ƒ(x) = bx.How does it differ from the…

A: Derivative rule for bx. The derivative of fx=bx is given by f'x=bx lnb.

Q: Find the average rate of change of h1x2 = x2 - 2x + 3:(a) From - 1 to 1(b) From 0 to 2(c) From 2 to…

A: Since it is known that the average rate of change can be calculated using the formula…

Q: at x: つ:8ー5x, atx=e

A: Given:  F(x) = x3 - 5x ...(1)       and the…

Q: If a function is decreasing with an upward concavity, what do you know about the function's first…

A: Given :   If a function is decreasing with an upward concavity To find : the function's first two…

Q: The net worth, ƒ (t), of a company is growing at a rate of f' (t) 1000 – 6t2 in dollars per year…

A:

Q: Find the derivative of the function. f(x) = ln(x2 + 3)

A:

Q: What is the instantaneous rate of change of the function f ( x ) = 5 /x  at x = 3 ?

A: Given,        The instantaneous rate of change of the function fx=5x at x=3.We know that,…

Q: Find teh average rate f change of f(x)=3x^(2)-x from x_(1)=-1 to x_(2)=2

A: Solution: The objective is to find the average rate of change of the given function

Q: compute the rate of Change of the functioN at x= a. flx)= -2X²-X,Q= -5 instantaneous

A: Given function: fx=-2x2-x

Q: Determine the instantaneous rate of change of the function f(x) x4 at the point where x = -2.

A: instantaneous rate of change of a function is differentiation of function at that point

Q: gives a good approximation, where t is time in years since 2007. Find the derivative function R'(t).…

A: The model representing the given data is defined by the function Rt=0.25t2-t+29 gallons, where…

Q: 1. What is the derivative of f(x) = x2 – 8x + 12 when you illustrate using tangent? 2. What is the…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: find the derivative of f(x)=sec(x^4)ln(9x-8)

A:

Q: Solve for the derivative of the function using chain rule. 6. f(x)= cot(6x3+5)

A: Derivative

Q: Let g(x)=7arctan(5x). What is the instantaneous rate of change of g(x) when x=2?

A: g(x)=7arctan(5x) to find rate differentiate g(x) with respect to x

Q: A bicyclist is riding on a path modeled by the function  f(x) = 0.04(10x − x2),  where x and f(x)…

A: given: A bicyclist is riding on a path modeled by the function fx=0.0410x-x2 where x and f(x) are…

Q: Find the derivative of the function. h(x) = ets. - x + 1

A: Differentiate w.r.t x

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Given,          The total cost in dollars from the production of x printers is given by…

Q: What is the average rate of change of f between x=3 and x=10

A:

Q: What is the average rate of change of f(x)= x2 -2 on the interval [-1,3]?

A:

Exponential Growth Model

The relation that represents an exponential function is: