A company introduces a new product for which the number of units sold S is given by the equation below, where t is the time in months. (Let t = 0 correspond to midnight January 1, t = 1 corresponds to midnight February 1, and so on throughout the year.) S(t) = 245(7-(7/(2+t))) where t is the time in months. a) find the average rate of change (in units/month) of S during the first year. Answer: ? units/month b) During what month of the first year does S'(t)equal the average rate of change? Answer: ?

Q: 3. Find an equation of the tangent line to the graph of y = log,x at the point ( 32,5).

A: We need to find the equation of the tangent line to the graph of y=log2x at the point (32,5) . Using…

Q: Daily crude oil production by one particular oil company for 2008-2013 could be approximated by P (…

A: The given function is Pt=0.009t2-0.7t+3.43. Compute the average rate of change of P ( t ) over the…

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: 1. Find the equation of the tangent and normal line to the curve f(x) =x' - 3x +2 at (1, 0).

A: Given the function f(x) :

Q: Find the slope of the tangent line to f(x) = e^[3 (x^2) − 4x] at the point (0,1).

A:

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

A: Given: h(x)=x2-2x+3

Q: 2. Find the equation of the tangent and normal line of the function y+ 3xy +x = 5 at the point (1,…

A:

Q: 4. Determine an equation for the tangent line to g(x) = 3 csc(x) – 2 at a = T/4.

A: Solution :-

Q: (a) Find the average rate of change of f(x) from x = 1 to x = 2. 7 (b) Using the definition of the…

A:

Q: 3. Find the equation of the tangent lines and the normal lines to the curve y = √2x-1 at x=5

A: As per the company guidelines we are supposed to answer only first question. Kindly repost the other…

Q: 2. Determine the equation of the line perpendicular to the tangent line to the function f(x) = e' at…

A: We will find the equation of the line.

Q: a new substance C is to be formed by removing two units from each of two substances whose initial…

A: 1st we will formed a differential equation for amount of C and then solve it to get actual amount of…

Q: If f is the focal length of a convex lens and an object is placed at a distance p from the lens,…

A: If f is the focal length of a convex lens and an object is placed at a distance p from the lens,…

Q: In a first order chemical reaction with no backorder reaction the concentration of the reactant is…

A: We solve for C(t)

Q: 1. Find the equation of the tangent line and normal line to the graph of y=√x² +3 at the point (-12)

A:

Q: The slope of the tangent line x = e*, y = In e3x

A: Let's find.

Q: The rate of change of the volume V(t) of blood in the aorta at time t is given byV′(t) =…

A: Given data:The rate of change of the volume V(t) of blood in the aorta at time t is given by…

Q: 4. on the interval [-1,3] find the average rate of change of g(x) = 8x +

A: The given function is gx=8x2+4x2, on the interval [-1, 3]. Note that, the average rate of change is…

Q: If the instantaneous rate of change of g(x) at (-1, -2) is 1/2, write the equation of the line…

A:

Q: 4. Find the equation of the tangent line to g(x) 8 at x = 3 |x²–1

A: The function is given by gx = 8x2-13 To evaluate: The equation of the tangent line to the graph of…

Q: A Cepheid variable star is a star whose brightness alternately increases and decreases. For a…

A: Given: A Cepheid variable star is a star whose brightness alternately increases and decreases. For a…

Q: If the instantaneous rate of change of g(x) at (−1, −3) is 1/2, write the equation of the line…

A: Slope of tangent line is ½. So the equation is of the form:

Q: Find the average rate of change of h(x)=x2-2x+3 (a) From -1to 1 (b) From 0 to 2 (c) From 2 to 5

A: Concept - If we have a function f(x) with x from a to b,thenAverage rate of change of function =…

Q: The sales of a new​ high-tech item​ (in thousands) are given by   ​S(t)=100−90e^−0.4t   where t…

A:

Q: A company finds that the rate at which the quantity of a product that consumers demand changes with…

A:

Q: 3. Find the equation for the normal line (perpendicular to the tangent line) to f(x) = 2x3 – 2x at x…

A:

Q: 5. Determine the average rate of change of f(t)=t – 2t in the interval 2,5|.

A:

Q: For the function f(x) = x² – 4 at the point (4, 12), find: a. the slope of the curve using the…

A:

Q: 3. Find the equation of the tangent and normal lines at the given value of x. 4 f(x) = x + - at x =…

A: Given, fx=x+4x at x=4f4=4+1=5The point is 4,5f'x=1-4x2f'4=34Slope of tangent line is 34Using…

Q: If the average rate of change of a function between x = a and x = b is negative, then is the…

A: The rate of change of function between two points of a curve represents the slope of the curve.   If…

Q: 3. For the function g(x) = x' - 2x -1, at what tangent point is the instantaneous rate of change…

A: Instantaneous rate of change of f(x) at x=a is given by f'(a), where f'(x) is the first order…

Q: 7. Determine the equation of the tangent to the function E-2 f(x)=- at x= 1.

A:

Q: Find the average rate of change of the function over the given interval. y=3x+ 1%3; between x= 1 and…

A:

Q: The line with the rule y = 3x + 4 intersects the curve with equation ¦(x) = x2 at the points (-1, 1)…

A: Given:- The line with the rule y = 3x + 4 intersects the curve with equation f(x) = x2 at the points…

Q: 6. Train E travels west toward Chicago station at 120 miles per hour while a second train N travels…

A: Train E =120 miles per hour  Train N=90 miles per hour

Q: A total cost function (in dollars) is given by C(x) = 116 + 3x + 0.37x. Use differentials to…

A:

Q: Suppose that f(x) = 3x² – 3. (A) Find the slope of the line tangent to f(x) at x = 5. (B) Find the…

A: We find f'(x) using the power rule Slope of the line tangent to f(x) at x=5 is given by f'(5) So to…

Q: Suppose that f(x) = 5x² – 4. (A) Find the slope of the line tangent to f(x) at x = 5. (B Find the…

A:

Q: Suppose yy varies at a constant rate of change of -0.6 with respect to xx (so that…

A:

Q: If f is the (constant) focal length of a convex lens and an object is placed at a distance p from…

A: Given,1f=1p+1qwhere f is focal lenrth and an object is placed at a distance p from the lens and its…

Q: Let m(x) be the slope of the tangent line to the curve y = 2x° – 6x² + 3x at the point (x, y). Find…

A: We have to find instantaneous rate of change of m(x) at point (2,-2)

Q: Let ​h(x)=x^2−8x.   ​(a) Find the average rate of change from 4 to 7. ​(b) Find an equation of the…

A: Average rate change and secan line problem....

Q: 9) Find the equation of the tangent line to: y = (1+x) e*when x=0

A:

Q: With assuming ideal laboratory conditions, the number of bacteria in a culture grows by the law Q(4)…

A:

Q: Let m(x) be the slope of the tangent line to the curve y = 2x³-6x² + 3x at the point (x, y). Find…

A: Given: y=2x3-6x2+3x

Q: find the function that gives the value of the investment as a function of t. (Round your value of k…

A:

Q: For the function y = (x2 + 2)(x3 - 9x), at (-3,0) find the following. (a) the slope of the tangent…

A: The given function is y=x2+2x3-9x. Differentiate fx with respect to x.…

Q: The cost in pesos of producing x units of a certain commodity is C(x) = 0.05x2 + 10x + 5000. What is…

A:

Q: Early one morning it began to snow at a constant rate. At 7 A.M. a snowplow set off to clear a road.…

A: