(a) Using practical examples from the field of calculus compare and contrast the concept of slope of a line and differentiation. Illustrate your understanding of these concepts by discussing and explaining possible two reasons for their differences using a practical case in mathematics.

Q: Find the slope m of the tangent line to the graph of the function at the given point and determine…

A: we will find the slope and equation of tangent

Q: (a) Use implicit differentiation to find if  x2+ x   y + y 2 +1 = 0 (b) Plot the curve in part (a).…

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Q: IN 15 MINUTES PLEASE calculus Find all points on the curve x^2y^2 + xy = 2 where the slope of the…

A: Solution is done in step 2

Q: f (x) = sec(x), x = 4

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Q: (a) find an equation of the tangent line to the graph of the function at the given point, (b) use a…

A: To find the equation of tangent, first find the slope by differentiating the function f(x)=12xlnx2…

Q: Using implicit differentiation, find the slope of the tangent line to the graph of the curve x^4 +…

A: Slope of the tangent is obtained by dy/dx

Q: Find an equation of the curve whose tangent line has a slope of f'(x)=x^7/9 given that the point…

A: Given : f'x = x79

Q: 2(x2+y2)2=25(x2-y2) Use implicit differentiation to find an equation for the derivative of the…

A: It is implicit differentiation.

Q: Please tell me how to solve below question. (2) find the equation of the tangent line to f(x)=…

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Q: (a) Use implicit differentiation to find an expression for (OR y') in terms of z and y. (b) Find the…

A: Differentiate y w.r.t. to x .

Q: Pregunta 8 Find the slope of the tangent line to the curve f(x) = x²(1 – æ)* at x = 2 Answer: The…

A: Product Rule of differentiation :   d(u.v)dx =u.dvdx+dudx.v

Q: Find the slope of the tangent line to the graph of f(x) = 5x at the point (4,80). Find the…

A: a)Given, f(x)=5x2 at the point (4,80) find the slope of the tangent line to the graph f(x)=5x2 at…

Q: (a) Find the slope m of the tangent to the curve y = 7/Vx at the point where x a > 0. m = (b) Find…

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Q: Uncover the function f shown that the slope of the tangent line to the chart of f at any point (x,…

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Q: 16. Which of the following statements is true? A. The slope of a line can be applied for curves or…

A:

Q: Find the tangent line, in slope-intercept form, of y=f(x) at the specified point. f(x) = - 5 3 2 -1+…

A: Given function, f(x)=5x-3x+2x2f(x)=5x-3x-12+2x-2

Q: Find the slope m and an equation of the tangent line to the graph of the function f at the specified…

A: Given:f(x)=x2x+7        at  (1,16)

Q: Using the definition of the slope of a tangent line, and find the slope of each function at x=c. 4.…

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Q: Find the equations of the tangent line and normal lines to the graph of the function f(x) = –10x – 2…

A: given function :

Q: y 4x + y - 9 y° + 27 y = 4: -10 -5 10 15 -2 (a) Which is greater, the slope of the tangent line at x…

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Q: Find an equation of a line that is tangent to the graph of f and parallel to the given line.…

A: Slope of the tangent line is the derivative of the given function. So differentiating f(x) with…

Q: Find two points where the curve x^2+3xy+y^2=47 crosses the x-axis. The tangent lines to the curve at…

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Q: Find the equation of a tangent line to the curve y= 2x3 - 3x² - 10x + 1 which is perpendicular to…

A: topic - equation of tangent line which is perpendicular to given line

Q: Find an equation of the line tangent to the graph of f(x) = (5x-9)(x + 6) at (2,8). The equation of…

A: F(x) = (5x -9)(x+6)  at point (2,8) here we have to find tangent equation  so tangent slope = slope…

Q: (a) Find an equation for the line tangent of f(x)= x^3+3x^2-2x-8, at the point where x=1. (B) There…

A: fx=x3+3x2-2x-8 When x = 1,  f1=13+312-21-8=-6 So we have to find the equation of the tangent line at…

Q: (a) find an equation of the tangent line to the graph of the function at the given point, (b) use a…

A: Given a function  y=ln x2/3, find an equation of the tangent line to the graph of the function at…

Q: date given f(x) = x³+4x² - 7 a. find f'(x). f(x) = %3D b. find the slope and equation of the tangent…

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Q: Find an equation of the line that is tangent to the graph of f and parallel to the given line.…

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Q: Richa< decline under question out of Scope> Find the equation of the tangent line to…

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Q: The slope of the tangent line at any point (x, y) on a curve is 2/x. If the point (9, 3) is on the…

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Q: Show the connection between the slope of a tangent of a function at a given point and its derivative…

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Q: 1. On what instance does the Chain Rule of differentiation applicable? Explain briefly. 2. How does…

A: Recall; COMPOSITE FUNCTION:  A Composite function is generally a function that is written inside…

Q: a. Find the slope of the tangent line to the graph of f(x) = x +4 at the point (- 1,5). b. Find the…

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Q: (a) Using a calculator or a computer program, find the best-fit linear function to measure the…

A: Ok, Inputs   we did the linear regression and found following results..    Actual plot :-

Q: implicit differentiation to find y ′. x2⁄3 + y2⁄3 = 4   Find an equation of the line tangent to the…

A: Given that           x2/3 + y2/3 = 4 Here we have to find y' by implicit differentiation and also…

Q: (a) Use implicit differentiation to find y' if x2 +xy +y2 +1  = 0.(b) Plot the curve in part (a).…

A: Given: To find the value of y’, differentiate both sides with respect to x,

Q: (a) Find the slope of the tangent to the curve y = 1//x at the point where x = a. (b) Find equations…

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Q: Numerical differentiation refers to determining the value of the derivative of a function at a…

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Q: A. Find the slope of the tangent line to the graph of f(x)=7x^2 at the point (3,63) B. Find the…

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Q: What can you say about the tangent line to the graph of f(x) = V+ 2- 3 at = -2? O There is no…

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Q: Find the equation of the line tangent to the graph of the given function at the point with the…

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Q: (a) Find the slope m of the tangent to the curve y = 3/Vx at the point where x = a > 0. m = (b) Find…

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Q: how do you find the  (a). equation of the scant line through the points wehre x has the given…

A: The given equation is f(x)=x^2+2x.

Q: Inclass (Example 3: Find the equation of the tangent line to the graph of f(x) = r³ +4 at r =-1.

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Q: Using the definition of the slope of a tangent line, find the derivative of each function. 1. f(x) =…

A: Given:- 1) f(x) = 2x - 6 2) g(x) = x2 + x - 1 3) h(x) = √(4x)  To find:- Slope of tangent line by…

Q: अ 250 -x5/2 - 2x³/2 + +बेकर 9 x³ - 2x² + x − 1 -

A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the…

Q: (a) Find the slope of the graph of f(x)=1-e" at the point where it crosses the x-axis. The slope is…

A: To find the equation of the line

Q: Find the slope of the graph of the function f(x) = /2x at (2,2). Then find an equation of the line…

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: