Q.2. A) For the function y f(x) whose graph is shown below, find the points of discontinuity and give the reasons of discontinuity at each point. y = f(x) 1 1 3.

Q: Determine the missing coordinates of the points on the graph of the function

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Q: Suppose the line tangent to the graph of f at x 3 is y 6x 5 and suppose y 2x - 2 is the line tangent…

A: The tangent line to the graph of f at the point x=3 is y = 6x + 5 and the tangent line the graph of…

Q: For what values of z does the graph of f(z) = 21 – 9z² – 60z – 1 have a horizontal tangent line?…

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Q: (3) Find the equation of the line tangent to f(x) = 2x³ - 2x2 +1 at x = 1. [Hint: f'(a) is the slope…

A: We find the slope of f(x) at x=1 by finding f'(1)

Q: 2. Let f(æ) = 2e* – 3x² /a, whose graph is given to the right. Sketch in the tangent lines to f(x)…

A: Graphed the tangents using a graphing calculator.

Q: Which of the following describes the behavior of the graph of y = |x² – 16| at x = 4: a.…

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Q: (a) If g(x) = x2/3, show that g'(0) does not exist.(b) If a ≠ o, find g'(a).(c) Show that y = x2/3,…

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Q: 4. The function b(x) = . is shown with the solid graph. Which dotted %3D curve could represent t(x)=…

A: We have to draw a graph.

Q: Given that f(2) =-7 and f'(2) = -8, find an equation for the tangent line to the graph of y = f(x)…

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Q: 20. Find the point on the curve y= /x that is closest to the point (3, 0).

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Q: There is no point on the graph of f(x) = 3x2 4 at which the tangent line is y = 12x- 2. Select one:…

A: We have to consider gi condition is true or false

Q: Suppose the line tangent to the graph of f at x = 4 is y = 6x +5 and suppose y = 5x-1 is the line…

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Q: Assume y = 3 · 5* is the equation for the blue line shown in the graph below, and that the black…

A: The equation of curve is:  y=3·5x

Q: - Find all k so that the graph of y = Er2 kx - + 9 is tangent to the x-axis. 4

A: We have to find all values of k such that the graph of this function will have tangent as x axis.…

Q: For the below function, find the stationary point(s) and prove if a maximum, minimum, or a saddle…

A: The given function is fx,y=-x2+6xy+y2-10x-5y. Compute the first and second partial derivatives as…

Q: find an equation of the Tangen line to the graph of y = e^-x^2 at the point  (2, 1/e^4)

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Q: 6. Find the length of the curve y =-+ from x =1 to x=2. 9. 28x

A: The curve is given by the equation, y=x99+128x7  and the point is given from x=1 to x=2. To find :…

Q: Find a function of the form y = Asin(kz) + C or y = A cos(kz) + C whose graph matches this one: -8…

A: The maximum point on the graph is at 3  . that is y intercept is at (0,3) When the maximum point is…

Q: The tangent line to the graph of y = g(x) at the point (4, 2) passes through the point (1, 8). Find…

A: topic - slope of a tangent line

Q: (a) If g(x) = x2/3, show that g'(0) does not exist.(b) If a ≠ 0, find g'(a).(c) Show that y = x2/3…

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Q: Suppose the line tangent to the graph of f at x = 4 is y = 5x +3 and suppose y = 3x - 5 is the line…

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Q: 5. If f(x) = ax* + bx' +cx² + dx +e, determine a, b, c, d and e so that the graph of f will have a…

A: 5) Given:   f(x)=ax4+bx3+cx2+dx+e As f(x) passes through origin (0,0) then substituting (0,0) in…

Q: If given f(3) = -1 and f'(3)=5, the tangent line to the graph y = f(x) at x=3 is y = 5x +16. (a)…

A: This question is based on finding tangent equation at a point on function.

Q: Show that, for any cubic function of the form y = ax + bx² + cx + d, %3D there is a single point of…

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Q: The function g(x) is obtained by shifting the graph of y=x2. (a) If g(3)=36, give a possible formula…

A: If the graph shifts horizontally, then the point (3 , 36) on the graph of g must correspond to a…

Q: Find dydx, where y is defined as a function of x implicitly by the equation below. y3+2x2y5=1

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Q: 41. Aroller coaster has the shape of the graph in Figure 19. Show that when the roller coaster…

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Q: Find the y-intercept of the line tangent to the graph of f(x) = 4/æ at x = 9. O 4 Answer not listed…

A: Slope of tangent is obtained by differentiating the function f(x).

Q: 2 For the graph of f(x) = ax + bx +4, the slope of the tangent at the point (3, 1) is 5. Determine…

A: Given that        f(x) = ax2+bx+4

Q: f(x) = + 3, X with 0 < x< 3

A: The length(arc-length) of the function is given by: L=∫ab1+(f'(x))2dx

Q: 9. Find the point on the curve y x² closest to the point (0, 1).

A: As per bartleby guidelines we only give first question answers.

Q: (a) If g(x) =x2/3 , show that  g'(0) does not exist.(b) If a≠ 0 , find g'(a) .(c) Show that y= x2/3…

A: Given function is gx=x23. Differentiating the function with respect to x,…

Q: Consider the following. 2 X- 3 x² - 3 x (a) Find the points of intersection of the curves. (x, y) -…

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Q: Suppose (P. 0) is the point on the graph of. y=Vx closest to (1, 0) - What is the value of p + Q? 3…

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Q: 13 Let f(x) 13 is 4 The slope of the tangent line to the graph of f(x) at the point 4, 13 The…

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Q: Let k (x) = 2x and consider its graph. %3D Find the slope of the secant line of this curve…

A: A secant line is a straight line joining two points on a function. It is also equivalent to the…

Q: Find an equation of the tangent line to the graph of y = B(x) at x = 24 if B(24) = −1 and B ′(24) =…

A: Given thaty=B24 x=24y=B24 =-1B'24 =-14To :find equation of tangent line Solution :equation of line…

Q: For what value(s) of x does the graph of 1 f(x) = – x² +3 have a .2 - horizontal tangent?

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Q: The graph of y = fx) and the tangent to the curve at x = 1 is shown below. ..... 5 3 y - f(x) -1 0.

A: Consider the given figure.

Q: Consider the point (x,y) on the graph of the line 6x+4y=7. Let L be the distance from the point…

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Q: At which point(s) does the graph of  y= e((x3-2x2+3x)/(x)) have a horizontal tangent line?

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Q: 1. Any function y = f(x) can be expressed as x = f(y) in standard mathematical methods for solving…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: For what value of c is the curve y = c/(x + 1)tangent to the line through the points (0, 3) and (5,…

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Q: Two vehicles start out traveling side by side along a straight road. T owing graph, are given by s =…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: (c) For what value(s) of x does the graph f (x) =3x³ – x² +3 have a horizontal tangent.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let f(x) = cos x. Sketch the graph of y = 2f (3x – 4) for 0<x < 67.

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Q: The graph of a function y = f(x) in the xy-plane is the set of all points _______ that satisfy the…

A: Given: The graph of a function y = f(x) in the xy-plane is the set of all points _______ that…

Q: Choose the correct graph of y = sin x, -"sxS T: 1 -37 21 -1 -2

A: The given function is: y=sin x ;                 -3π2≤x≤π

Q: Q2)B/ Find the points on the curves y(X) given by y = x - 6x? + x+3 where the tangents are parallel…

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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: