What function measures the rate of change of distance?

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

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Q: Find the rate of change. The diameter of a circle with respect to radius

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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: Determine whether each of the following statements is true or false, and explain why. The slope of…

A: We know that slope of tangent gives the instantons rate of change of given function and slope of…

Q: How do you find the fifth derivative of a function?

A: To find the derivative we differentiate the function once.  To find the second derivative we…

Q: Explain tangent function.

A: Given: Explain tangent function

Q: Describe the parallels between finding the instantaneous velocity of an object at a point in time…

A: We have to find out the parallels between finding the instantaneous velocity of an object at a point…

Q: Find the slope of the line Express the slope as a rate of change with the popular unit attached

A: We know that slope is the ratio of vertical and horizontal change between two points. Slope of the…

Q: Two straight roads intersect at right angles. A car is traveling south toward the intersection while…

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Q: ick is increasing at a rate of 3 meters per minute. How quickly is the area changing when the oil…

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Q: Why is the derivative of a constant function zero?

A: Consider the constant function fx=k. Apply the derivative definition as follows.

Q: The Gateway Arch in Saint Louis is modeled by the curve: y = 210 − 20 cosh ( x/30) . At what height…

A: yx = Height of the Gateway archyx = 210 - 20coshx30         Blue curve---------------------formulae…

Q: Find the second derivative.

A: Given that : The function is f(x) = 6 x10 - 17 x5 - 12 x3 + 5.

Q: boy 5 feet tall walks at a rate of 3 feet/sec towards a streetlamp that is 12 feet above the ground.…

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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: How can you use directional derivatives to estimate change?

A: Let f be a differentiable function. The directional derivative of f in a particular direction at a…

Q: Find the first, second, and third derivative.

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Q: If we know the rate of growth of a patch of moss, how can we calculate the area the moss covers?

A: The rate of growth of a patch of moss is modeled by a complex function A't, where t is measured in…

Q: What is the range of the tangent function?

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Q: Explain why the slope of the tangent line can be interpreted as aninstantaneous rate of change

A: The average rate of change of a function fx over the interval x, x+h is the slope of the secant line…

Q: Determine the rate

A: a.)Let the radius of the balloon = rRate at which the radius of the balloon is decreasing = drdt =…

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: DERIVATIVE

A: We have to find the third derivative of  given function

Q: estimate the instantaneous rate of change at the point indicated

A: To find the instantaneous rate of change we will find y'(x) We use the power rule

Q: What is the derivative of a constant function?

A: The derivative of constant function is always zero.

Q: What is the average rate of change of the height of the plant between Week 4 and Week 12, in inches…

A: Given:  Week Height (in inches) 4 24 6 27 8 30 12 48

Q: Explain the difference between average velocity and instantaneous velocity.

A: Given: Average velocity and Instantaneous velocity. To find: Difference between both velocity.

Q: The slope of the line through the distinct points (x1, yı) and (x2, Y2) can be interpreted as the…

A: To Determine: the slope of the line through the distinct points can be interpreted as the rate of…

Q: What's the difference between average velocity and instantaneous velocity?

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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: Acceleration is the first time derivative of velocity

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Q: 4

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Q: The rate of change of the area enclosed between the circle and the square is square meters per…

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Q: The rate of change of the temperature of a building is 7° /hr when the temperature is 12°. What is…

A: The rate of change of temperature per hour = 7o   The rate of change of temperature in 30 min or…

Q: Find the slope of the line Express the slope as a rate of change with proper unit attached

A: We know that slope is the ratio of vertical change to the horizontal change. The slope of a line…

Q: Are the instantaneous rates and slopes of tangent lines closely connected?

A: Are the instantaneous rates and slopes of tangent lines closely connected?

Q: the length of a rectangle is increasing at a rate of 2 feet per minute, and its width is decreasing…

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Q: According to Boyle's law, which graph shows the relationship between the pressure (æ) and volume (y)…

A: option c is correct.

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: Find the rate of the change of the function f(x)=-cscx-sinx

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Q: What is the velocity of flow in feet per seconds f

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Q: How do some functions vary continuously?

A: Given: Behaviour of the functions which vary continuouslyFor instance:…

Q: The radius of a right circular cylinder is increasing at the rate of 3 inches per ninute and the…

A: Given:The rate of change in radius =3 in/mThe rate of change in height =4 in/mThe radius =9 The…

Q: Find the instantaneous rate of change cope of the tangent line to 2 (3,-2) 1

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Describe the Derivative of the Natural Logarithm Function?

A: We have asked to describe  the derivative of the Natural Logarithm Function.

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,…