Scientists have found a relationship between the temperature and the height above a distant planet's surface.  Th , given below, is the temperature in Celsius at a height of  h  kilometers above the planet's surface. The relationship is as follows. T(h)=30.5-2.5h     a. T^-1(x)= b.T^-1(33)=

Q: Explain how the first derivative of a function determines where the function is increasing and…

A:

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: Describe geometrically when a function typically does not have a derivative at a point.

A: To describe geometrically when a function typically does not have a derivative at a point.

Q: What is the shape of a graph in application of derivatives?

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Estimate the instantaneous rate of change at x=2

A: Please refer to the image below

Q: Sarah is asked to find the maximum value of a function. Not having a complete understanding of the…

A: If we want to find the maximum or minimum values of a function then follows the steps mentioned…

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: What is the meaning of a derivative?

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Q: pimplicit derivativeg

A: we have to find the derivative of the given implicit function

Q: What are the maximum and minimum values in application of derivatives?

A: We have to define the maximum and minimum values in application of derivatives.

Q: What role does the derivative play in defining slopes, tangent lines, and rates of change?

A: To determine the role of derivative of a function in defining slopes, tangent lines and rate of…

Q: What function measures the rate of change of distance?

A: _____ function measures the rate of change of distance

Q: What information about a graph can be found from the second derivative?

A: What information about a graph can be found from the second derivative?

Q: A bicyclist is riding on a path modeled by the function f(x)=0.04(8x-x^2) , where x and f(x) are…

A: Given path functionfx=0.048x-x2

Q: Find the derivative of y= 4tan5α

A:

Q: How do you find the derivative of a constant multiplied by afunction?

A: If f(x) is any function and let y=cf(x)            function f(x) multiplyed with a constant, c is…

Q: бх + 5 -, is 10х + 8 The derivative of y =

A:

Q: Explain what happens when the derivative of a differentiable function is zero ?

A: To explain when a derivative of differentiable function is zero.

Q: Find the derivative.

A: Given: To find the derivative of y=2x-3-xx

Q: What is the derivative of the exponential function ex? How does the domain of the derivative compare…

A: To determine the derivative of the function ex and domain of the derivative.

Q: FIND THE THIRD DERIVATIVE OF A FUNCTION

A: Given, The function  fx = 11x2+9x-723x-5x2 We have to find the third derivative of the function.

Q: The slope of a tangent line at a given point on a curve tells the rate of change for the function at…

A: Let the given curve be f(x) -  Then f'(x) will be the slope of a tangent line at a given…

Q: Find the derivative. y = (lnx) 2

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Q: What is the derivative of a constant function?

A: The derivative of constant function is always zero.

Q: Discuss the solution on how to get the derivative of the function

A: This question is related to differentiation, We will solve it using given information.

Q: calculate the derivative y = ecosh−1 x

A: Given The chain rule of derivative is given by: The derivative of the inverse hyperbolic function…

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: Find the first and second derivative if w = 3z-2-(1/z)

A:

Q: Find the second derivative of

A: if you find my answer helpful please put thumbs up. thank you. the required solution is given below

Q: one leg of a right triangle is 1 in/min and the other leg increases 2 inches per min. What is the…

A: Let the first leg of the right triangle be a and the other leg be b. Let the hypotenuse of the right…

Q: What rule should be used in getting the derivative of y=(1−x^2 )^6

A: What rule should be used in getting the derivative of y=(1−x^2 )^6

Q: The number of live births recorded and the number of infants died in a town during a given period…

A:

Q: A research was done to study the effect of ambient temperature, x, on the electric power consumed,…

A: Solution

Q: Find the most general anti-derivative

A:

Q: Find the derivative

A: Given function - y = 10x5-2x3+4x-9x-10y = 10x5-2x-3+4x-9x12-10x0Using differentiation formula -…

Q: What is the derivative of y = 3lnx) Y :

A:

Q: Calculate the derivative. y=3/log5x

A: Given function is

Q: y = x-12; (4,) Use the derivative feature of a graphing utility to confirm your results.

A: We will solve the following

Q: Draw the graph with the first derivative

A: Draw the graph with the first derivative

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: The Climatologist that is working in the cave is trying to determine the age and growth rate of…

A: Given: Age, x Length in Micrometers, y 76 7906 87 9043 97 10091 104 10808 106 11024…

Q: 3 y = х-5

A:

Q: Find the derivative of the function. y = eV7x2- 9

A: y=e7x2-9 To Find: Derivative of the function

Q: Explain how the instantaneous rate of change of a function at a point is related to its average…

A: Instantaneous rate of change: The instantaneous rate of change is the change in the rate at a…

Q: us to find the derivative of x) = Vt3 + 27dt -3

A:

Q: Find the first derivative by increment method. Show your complete solution. V12x – 3 Irolim Exam…

A:

Q: If an object is shot upward from the ground with an initial velocity of  v0  feet per second, then…

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Q: How do you find the derivative of the quotient of two functions that are differentiable at a point?

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Q: What is the definition of the derivative (Difference Quotient)?

A: 2. What is the definition of the derivative(difference quotient)? ans. In single-variable calculus,…