Explain how the real-world meaning of a derivative is related to the independent (input) and dependent (output) variables of the problem. Use your explanation in a real-world contextual situation of your choosing. Also, include a sketch of the two axes (independent and dependent) that you use to help clarify your discussion for the reader. Please explain and sketch a graph of two axes.

Q: Explain why the derivative of x2+ y2 + 2 = 1 does not mean anything ?

A: x2+y2+2=1

Q: State the derivative. Do not simplify. f(x) = = x² +3 R

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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: What is the derivative of y= 2^x + x^2 / x-3

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Q: Find the derivative of the function.

A: y=(7x+3)4

Q: Find the equation of the tangent line to the graph of f(x) = -2(3x – 1)³ at . Show work or explain…

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Q: Explain in words how to evaluate the derivative of function?

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Q: f(x ) = x -3 х 2—9

A: Simplify the function then take derivative and draw the graph.

Q: Explain why the derivative of x2 + y2+ 2 = 1 does not mean anything ?

A: It is known that Derivative is defined only for functions.

Q: Find the derivative of the function.

A: Given y=2x-73

Q: x5/2+4 x3 y = 3

A: We have to find the derivative of the given expression: y=x52+4x3x3 Simplifying the given…

Q: Could f(x) be the derivative of g(x)? Please explain why or why not

A: Given graphs of f(x) and g(x)

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: A student performed data analysis to determine the relationship between the births attended by…

A: This is output of polynomial regression and the model Is Good fit. We can easily find a relationship…

Q: Find the derivative, but do not simplify your answer. 2 3 y = (x + x + 4)Vx – 2/x + 7 -

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Q: Find the derivative of the function using shortcut rules. Simplifyfor extra credit. f(x)= (x2+ 4x)5

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Q: Is the function above differentiable everywhere? Explain using derivatives.

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Q: Explain why the derivative of x2 + y2 + 2 = 1 does not mean anything.

A: x2+y2+2=1 On simplification, we get ⇒x2+y2=1-2⇒x2+y2=-1 This curve does not exist as the sum of two…

Q: Write the equation of the line tangent to the graph of the function at the indicated point.…

A: To find the equation of the line tangent to the graph of the function y=x2-5x+55x0,y0=4,1

Q: I need help with finding the derivative.  y=(2x^2   +   1)^2   (x-1)^3

A: Given: y=2x2+12x-13 We know that ddxu.v=vdudx+udvdx…

Q: Why are both the x-coordinate and the y-coordinate generally needed to find the slope of the tangent…

A: Given,           The x-coordinate anf y-coordinate generally needed to find the slope of the tangent…

Q: Calculate the derivative of the function y=(√3)2−5√2.

A: Given : the function is given as y=32-52 Now, we know that the derivation of constant function is…

Q: In your own words, state the guidelines for implicit differentiation.

A: We have to state the guidelines for implicit differentiation.

Q: Write the equation of tangent line to the graph of y= x^2-9x/3x-x^3 at x= 3. Chex the reasonableness…

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Q: What do the derivatives of a function tell you about the shape of its graph?

A: If the first derivative is positive, then the graph increases. If the first derivative is negative,…

Q: Give examples of still other applications of derivatives.

A: Derivatives have various important applications in Mathematics such as:Rate of Change of a…

Q: Find an equation of a line that is tangent to the graph of f and parallel to Function Line f(x) = x3…

A: In this question we will use basic of calculus i.e concept of application of differentiation. We…

Q: How do you use the second derivative test to analyze concavity of a function?

A: We know that, If the second derivative of the function f(x) is defined on an interval (a,b) and…

Q: Give information on this application of derivatives:  Optimization

A: Topic:- application of derivatives

Q: find the equation of the line tangent to the graph of y=3ln⁡(x) at x=3. Tangent Line:…

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Q: Find the equation of the line tangent to the graph of f(x) = x² + = - 9 at x = 7. y = help…

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Q: Make 2 examples (problem solving) regarding maximum and minimum values (application of derivatives.

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Q: what are the real-life applications of derivatives?

A: Definition of derivatives helps to find real-life applications. Functions obtained after the…

Q: Please provide an example of real life computation and application of derivatives

A: Follow the steps.

Q: What information can be obtained from derivatives? Please provide 2 examples from the real world and…

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Q: What can be said about the relationship between the graph of a  function and the tangent line at a…

A: The point where the second derivarive of graph is zero is called graph of inflection.

Q: -2x sinky sitlecex) -10

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Q: Why are derivatives important in our daily lives?

A: Why are derivatives important in our daily lives?

Q: Help finding the derivative.   y=(x^-2+x)^-3

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Q: Explain derivatives on optimization ?

A: Topic:- derivatives

Q: Need to know the steps to get the derivative of (x-2)(x-10)^3

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Q: Find the derivative, but do not simplify your answer. y = (7x6-5x4 + 2x² − 1)(4x8 + 3x6 – 5x² + 4x)…

A: As we know that: The product rule: f·g'=f'·g+f·g' The Power law: ddxxn=nxn-1 Given:…

Q: Why are both the x-coordinate and the y-coordinate generallyneeded to find the slope of the tangent…

A: In implicit differentiation, the result of derivative of the curve that often contains the dependent…

Q: ______ provide a means to predict the value of a function at one point in terms of the function…

A: Given: Let us consider the given statement, "______ provide a means to predict the value of a…

Q: What do you look for when you need to match the graph of a function with the graph of its…

A: Observe the behavior of graph as the value of x increases.

Q: Implicitly derive all variables in terms of x. Equate the derivative in terms of y'. Simplification…

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Q: True or false, for the graph of y=2^x, the slope of the tangent line is the same as the function…

A: slope of tangent line to a curve y = f(x) is given by          m = dydx