For the function y= 9x^2+8x+4,at the point x=4, find the following (A) the slope of the tangent to the curve (B) the instantaneous rate of change of the function

Q: 2. how does the knowledge of differentiability and continuity determine the derivative of functions?

A: A function is said to be differentiable if the derivative of a function exists at all points. The…

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

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A: The line x = 7 is perpendicular to x axis. Hence, it's slope is infinity. The tangent line that is…

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Q: The rate of change of atmospheric temperature with respect to altitude is equal to the slope of the…

A: The rate of change of atmospheric temperature with respect to altitude is equal to the slope of the…

Q: at the point (2, –1). Find the maximum rate of change of f(x,y): x2 + Y

A: For maximum rate of change we need to calculate magnitude of gradient bat point (2,-1)

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: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

A: Given that a company can produce 12,000 units when the number of hours of skilled labor y and…

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: The slope of the tangent line to the graph of f(r) at the point (-7,5) is The equation of the…

A: Topic - equation and slope of tangent line to curve

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: Consider the constant rate of depreciation value of a certain car. You bought a car amounting to 1.5…

A: Solution

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Given,         The total cost in dollars from the production of x printers is given by…

Q: Match the graph of the function with the graph of its derivative.

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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: Explain in 200 words the relationship between the secant line, slope of the tangent line, derivative…

A: Given: secant line, slope of the tangent line, derivative of a function using the limit process,…

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 4th derivative of the function y=exsinx.

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Q: Explain the relationship between the slope and the derivative of ƒ(x) at x = a.

A: Given function is  fx at x=a

Q: 3. Tak-gu baked 10 loaves of bread in 1 hour. After that, he baked a dozen of bread in 80 minutes…

A: We have three points,  A = (60 min, 10 )  B = (80 min, 12 )  C = (90 min, 12)    Hence, we have…

Q: Find the derivative at the point (0,.5) x2+y2=(2x2+2y2-x

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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…

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A: Given query is to find the time when output will become one fifth of initial value.

Q: How to solve for the second derivative?

A: The objective is to solve for the second derivative. Consider a function fx=3x4

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

A: Given: Let f and g be two differentiable function at point x.

Q: average rate of change

A:

Q: Show that the rate of increase in the slope of the tangent at a point on the curve y = 2x3 is 12…

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Q: 1. Describe the relationship between the derivative of a function to the slope of the tangent line.

A: Query- Describe the relationship between the derivative of a function to the slope of the tangent…

Q: What is the rate of change of the function whose graph is a line passing through  (3, 5) and (−1,…

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Q: Find the slope of tangent line for the equation x^2+y^2=5 on (1,2)

A: The given equation of the line is,

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

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Q: The slope of the line through the distinct points (x1, y1) and (x2, y2) can be interpreted as the…

A: The slope of the line through the distinct points (x1, y1) and (x2, y2) is defined as…

Q: State the second-derivative test for functions of two variables.

A: State the second - derivative test for functions of two variable.

Q: If we have a formula giving the cholesterol level of a patient as a functionof time, how can we find…

A: Integration gives the function whose derivative is given. Integration means adding all slices to…

Q: 2 2. f(x) = 5-x², (3,-4)

A:

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Given,          The total cost in dollars from the production of x printers is given by…

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: Find the derivative of the function at Po in the direction of A. txу) - - ху + у, Р,(10, - 2),…

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Q: Find the slope of the tangent line to the curve defined by 3x^3 - 7xy - 7y^6 = -1599 at the point…

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