The function given by A(t)=0.0295t3−0.461t2+1.739t+5.73​, 0≤t≤10​, can be used to estimate the​ amount, in billions of​ dollars, invested by large oil companies in exploration for new reserves t years after 1995. Find the relative extreme​ points, and sketch a graph of the function.

Q: The projected number of senior citizens in the U.S. for the years 1995 through 2030 can be modeled…

A: Given: Nx=0.03x2+0.315x+34.23x is no of years after 2000

Q: 8) Sketch the function with the zeros (x + 3) (x=1) (x= 2)and: the y-intercept of -6. After doing…

A: To sketch the graph of the given function.

Q: Find the second order derivative of f(x) exsinxcos2x

A:

Q: The demand x is the number of items that can be sold at a price of Sp. For x=p* - 2p³ + 500, find…

A:

Q: Differentiate the function. y = etan(θ)

A: Given y=etanθ Use chain rule of differentiation to differentiate the given function.

Q: find the slope of the tangent line to the graph of the following function at the given point fx…

A:

Q: ) Find an CIuation of the line tangent to the graph of Gec)=6e3X x tal dou2 o the Point (0,6). at

A:

Q: Find the slope m of the line tangent to the graph of the function f(x)=9-x^2 at point P(4,-7).

A:

Q: The slope of a tangent to the curve f(x) = x² + 2x – 5 at the point (3, 10) is : 12 8. -5 10

A:

Q: The function f(x) = x2 describes the area of a square, f(x),in square inches, whose sides each…

A: Given: fx=x2. Here, fx describes the area of a square in square in inches

Q: Starting from the point (, 1), at which direction does the above function f decrease fastest (most…

A: fx,y=esinx y     π6,1

Q: A company has determined that its price-demand function for its sale of its product is given by…

A:

Q: The slope of the curve f(x)= at x =1 is

A: given function :

Q: The function f(x) = x2 describes the area of a square, f(x), in square inches, whose sides each…

A: Given function fx=x2 To find rate of change of area.

Q: A long distance company charges a monthly fee of $4.95 and $0.02 per minute. Let f(x) be the monthly…

A: Solution:

Q: A property agent handles an office building with 50 identical offices for rental. Experience shows…

A: Consider the given scenario. Number of offices = 50. When the monthly rent per office is $800, all…

Q: How can you use the slopes of tangents to determine whether a function is increasing, decreasing, at…

A:

Q: Find an equation for the line tangent to the graph of  f(x)= 2xex at the point (3,f(3)). y=?

A:

Q: Q3. Find any local maximum and local minimum values, and then sketch the curve by using 2-1 fx =…

A: Given: The function fx=x2-1x2+1 To find: Local maximum and local minimum values, To Sketch: The…

Q: For the function y= 9x^2+8x+4,at the point x=4, find the following (A) the slope of the tangent to…

A:

Q: Find the rate of change of the function at a given value. 1. f(x) = 2x – 3, at x = 5 2. f(x) = 2x² ,…

A:

Q: The slope of the tangent line to the graph of the function y = 9/ – 2 at (4, 16) is - -5.00 2.25…

A: To find the slope of the tangent line for the given function at (4,16)

Q: 10. Find a function y = ax +bx+c whose graph has an x-intercept of 1, a y-intercept of -2, and a…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: What is the slope of the line tangent to the graph of g(x)=1/x at x=1?

A: Given that ,         g(x)=1x          find slope of tangent at x=1

Q: Match the graph of f, below, with that of its derivative. -2 -1 1 2 3 4 1- -2 4 6 -4+ -3- -6+

A: This question is related to Functions and its derivative, we will solve it using given information.…

Q: 800 Compute the average rate of change of the function, f(x) =5x²–9x - x2 over the interval [4,10].

A:

Q: slope m of the line tangent

A:

Q: Suppose the derivative of the function y = ƒ(x) is y′ = (x - 1) 2(x - 2)(x - 4). At what points, if…

A: It is given that, the function f(x) has the derivative

Q: Find the equation of the tangent and normal line of the function f(x)=√2x-1 at the point (5,3)

A:

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: Given : C(t) = 8(e-0.4t - e-0.6t)   To find the maximum concentration of the antibiotic during the…

Q: Estimate the derivative of the function f (x) = - – 3 at the point x = 3. 3 3 1/5 1/3

A:

Q: Find the slope of the line that is tangent to the 2x-3 graph of f (x) at P(3/2, 0)

A: Slope of the tangent to tthe curve y=f(x)  at point (a,b)  is given as m=f'(a)

Q: The size of a population of butterflies is given by the function. p(t)= 6000/(1+49(0.6)t) where t…

A:

Q: How fast does the  slope of the curve y= (x2+x+1)2 change at the point where x=2

A: First derivative of a function represents the change in function or slope of the function and second…

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: As machines get older, the cost of maintaining them tends to increase. Suppose for a particular…

A:

Q: On May 9, 2007, CBS Evening News had a 4.3 point rating. (Ratings measure the number of viewers.)…

A: Considering p be the rating point and f(p) be the revenue earned in millions of dollars.

Q: 3. Find the slope of the curve of the function y = at the point P (2,-).

A:

Q: 4, A vehicle was traveling along a straight way. The velocity as a function of time is modeled by…

A: Note: We are authorized to answer one question at a time, since you have not mentioned which…

Q: 6- For the function y=lnx a- Describe what type of function it is. b- How is the function related to…

A:

Q: Find the average rate of change and the equation of the secant line for 2x f (x) = from -1 to 3. x²…

A:

Q: There is a bacteria cell in a Petri dish that is reproducing at a rate of              r(t) = 2t^2+1…

A: Solution:

Q: The average number of vehicles waiting in a line to enter a parking ramp can be modeled by the…

A: Differentiating f(x) with respect to x by dividing rule

Q: The pressure of the oil in a reservoir tends to drop with time. By taking sample pressure readings…

A: Given that

Q: The slope of the line tangent to the graph of position as a function of time at t = to

A: The slope of the line tangent is in the form of a difference quotient approach t=t0 is, m=ft-ft0t-t0

Q: Differentiate the function.

A: Given: y=ex1-ex

Q: The crime rate of a certain city is decreasing by exactly 3%each year. Let t=0 correspond to the…

A: The function that represents the continuous decrease in number of crimes is given by:

Q: Estimate the slope of the tangent to the function f(x) = (x + 1)^2(x - 4) at the point of abscissa…

A: Introduction: A tangent line is one that intersects a curve at the so-called point of tangency.…

Q: The amount of vegetation eaten in a day by a grazing animal is a function of the amount V of food…

A: Given relations are S=2.8-2.8e-0.01vH=0.2-0.2e-0.006v where S and H are daily intake of sheep and…

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.