1 1. Given that y =- a. Find the average rate of change of y with respect to x over the interval [2,3]. b. Use the limit definition to find the instantaneous rate of change of y with respect to x at x, = 2.

Q: (a) The marginal revenue of a company is given by MR = 100 + 20Q + 3Q2 , where Q is amount of units…

A: We can find TR(total revenue) by integrating MR(marginal revenue) with respect to Q(price).

Q: Suppose that f(t) = 3t + 2 – 12t. а. What is the average rate of change of f (t) over the interval 2…

A: We are given the function f(t) = 3t+2-12t => f(t) = 2-9t. For (a), The average rate of change of…

Q: Consider the following function. 1 f(x) Find its average rate of change over the interval [4, 16].…

A: Given:  fx=1x  To Find:  The average rate of change of the function over the interval 4, 16=?…

Q: 1) Find the average rate of change of the function over the given interval. a) f(x) = x³ + 1, [2,3]…

A:

Q: Suppose that z =x*y°,where bothx and y are changing with time. At a certain instant when x = 1 and y…

A: Derivative formula ddxxn= n xn-1Product ruleuv'=u'v+uv'

Q: Suppose that z = x*y°, where both x and y are changing with time. At a certain instant when x = 1…

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

Q: If (X1. (x1)) and (x2, f(x2)) are distinct points on the graph of a function f, the average rate of…

A:

Q: Suppose an object moves along the y axis so that its location is y = f(x) = x² +x at time x (y is in…

A: The position of the object at time x is y=f(x)=x2+x (A) The average velocity for x changing from 5…

Q: 5. If a ball is thrown into the air with a velocity of 40 ft/s, its - 401- 16r. height in feet…

A:

Q: Find the average rate of change of the function over the given intervals. h(t) = cot t 5π7π а. 4 ' 4…

A:

Q: Consider the following function. f(x) = Find its average rate of change over the interval [1, 9]. Ду…

A: The given function is -  f(x) = 1x We have to find the following -  (a) Average rate of change over…

Q: Given the following function, determine the maximum rate of change of it at the point P(0,0, 1/2).…

A:

Q: Find the average rate of change of the function over the given interval. f(t) = 4t + 8, [3, 4]…

A: Given ft=4t+8Average rate of change of function within a,b is given by ,=fb-fab-a

Q: 2.1 Suppose that f (t) = 3t + 2 – 12t. а. What is the average rate of change of f(t) over the…

A: Given : f(t) = 3t + 2 - 12t To find : a. What is the average rate of change of f(t) over the…

Q: Find the average rate of change of the function over the given interval. f(t) = 6t + 9, [2, 4]…

A: The derivative of the function gives the instantaneous rate of change of the function. since the…

Q: For a function f, we define the ___________________________________, denoted f’, by…

A:

Q: suppose that g(s)=s^2+3s+4 . find a value c in the interval [0,2] such that g'(c) equals the average…

A:

Q: 4. Find the equation of the tangent line and the normal line to the graph of the given function at…

A:

Q: Suppose g(s) = s2 + 4s +1. Find a value c in the interval [1, 11] such that g'(c) equals the average…

A:

Q: 1. Determine the value of so that the average rate of change of the function h(x) = x + 3x+2 on the…

A:

Q: Consider the following function. g(x) = x³ – 5 Find its average rate of change over the interval…

A:

Q: Given f(z)= + 12r, find the average rate of change of f(r) on the interval (1, 1 th, Your answer…

A:

Q: Calculate the appropriate limits to find the following: (a) The instantaneous velocity at time t = 4…

A: (a) compute the instantaneous velocity at time t=4 as follows. Take ft=t+22-1. Its derivative is…

Q: 1. let s(x) = 1.1 Find the average rate of change of s(x) with respect to x as x changes from…

A:

Q: Suppose that f(t) =t+4t-4. W.at is the average rate of change of f(t) over the interval 3 to 4? %3D…

A:

Q: From the following answer what is asked: f(x,y) = x√y ,(2,4), v = 2i - j d) In which direction is…

A:

Q: What limit must be calculated to find the rate of change of a function g(t) at t = t0?

A: The rate of change of a function g(t) at t = t0 is given by g'(t0).

Q: Find the average rate of change of the function over the given interval f(t)=2t+3    [4,6] =…

A: Consider the given function: ft=2t+3 ; 4,6 Here, the objective is to find the average rate of change…

Q: Consider a function y = 1 / x a) Find the rate of instantaneous change of y with respect to x at x…

A: a) y = 1 / x dy / dx = - 1 / x2

Q: Let y = x + 5. (a) Find the average rate of change of y with respect to x over the following…

A:

Q: Suppose that f(t) =t +t-5. What is the average rate of change of f(t) over the interval 4 to 5? The…

A:

Q: The average rate of change of y with respect to x over the interval [0, 3] for the function y = 3x…

A: The function y=3x+2 over the interval 0,3

Q: Consider the following function. g(x) = x³ – 5 Find its average rate of change over the interval…

A:

Q: Given the following function, determine the maximum rate of change of it at the point P(0,0, 1/2).…

A:

Q: Let y = x2 + 7. (a) Find the average rate of change of y with respect to x over the following…

A:

Q: 4. Let f(x) = 3r2 – 2x + 1. (a) Find the average rate of change of f(x) on the interval [1,3]. (b)…

A:

Q: Consider the following function. h(x) = 5 - 2x Find its average rate of change over the interval [1,…

A:

Q: Find the average rate of change of the function over the given interval. f(t) = 4t2 – 1, [1, 1.1]

A: Given data: The expression for the function is f(t)=4t2-1. The given limit of t is [a, b]=[1, 1.1].…

Q: If y=f(x) and x changes from x1 to x2 , write expressionsfor the following.(a) The average rate of…

A:

Q: Consider the function y=x/x-1  , where the unit for x is hours and the unit for y is km. a)…

A: Use formula to calculate

Q: 11. True or false: If the function f represents position (height or displacement), then the…

A:

Q: (a) Calculate the average rate of change of R with respect to q over the intervals 1 < q< 2 and 2 <…

A:

Q: -4 to x = 1 Find the average rate of change of g(x) = 3x° - 1 from z =

A: Average is (g(1) -g(-4)) /5

Q: Consider the following function. 1 f(x) Find its average rate of change over the interval [1, 4]. Ду…

A: Solve the function

Q: The graph below shows the relationship between the height of water in a bottle (in inches), h, and…

A:

Q: 4. Suppose the function is defined by y = f(x) = x² – x a. Find the average rate of change of y with…

A:

Q: 4. Suppose the function is defined by y = f (x) = x² – x a. Find the average rate of change of y…

A: y=fx=x2-x a). The average rate of change of the function over the interval 1, 3 is,…

Q: 1. Consider the function f(x) = 2x² – 3x +4. a) Determine the average rate of change between the…

A:

Q: From the following answer what is asked: f(x,y) = x2 e-y , (3,0), v = 3i + 4j d) In which…

A:

Q: Consider the following function. 1 f(x) = Find its average rate of change over the interval [4, 9].…

A:

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.