Passage III (Q. Nos. 30 to 32) If y = f(x) is a curve and if there exists two points A(x1, f(x1)) and B(x2, f(x2)) on it f(x2) – f(x;) such that f' (x1)=- f' (x2) then the tangent at x, is normal at x2 for X2 - X1 that curve. Now, answer the following questions 30. Number of such lines on the curve y = sin x is

Q: The point on the curve y = 2-x nearest to (3,2) is (1,1) (0,2)

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Q: Construct the inverse matrix (if it exists) for the following matrices: [12 61 (а) А %— 4 2. 1 -2]…

A: We will find out the required solution.

Q: The tangent line to the graph of y = g(x) at the point (3, 6) passes through the point (1, 3). Find…

A: Please see the explanation below..

Q: Find all points (x,y) on the graph of f(x) = 2x3 + 1 with tangent lines perpendicular to the line y=…

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Q: A ball is drawn randomly from a jar that contains 5 red balls, 7 white balls, and 4 yellow balls.…

A: From the given information, there are 5 red balls, 7 red balls and 4 yellow balls. The total number…

Q: Find a point on curve y = (x-3)2 where the tangent is parallel to the line joining (4,1) and (3,0)

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Q: 2) Find the tangent equation for the function f(x) = x² + 5x at the point (1,4). *****: **********

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Q: 8. On a graph of f(x) = x², (a) draw the tangent line to the graph of f at the point (2, f(2)); (b)…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: tS W C (b) Suppose that a function h is such that h(-1) 5 and h'(x) 2x +3. Find the equation of the…

A: The derivative of the function h(x) is given by,

Q: Find an equation of the tangent line at the point P = (l, 1) on the curve in Figure with equation

A: Given figure is  where equation of curve is  y4+xy=x3-x+2

Q: If the Suppose the slope of the tangent line at any point on a curve is x2+4y² curve passes thru…

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Q: 3) Find all points (x, y) on the graph of x2/3+y²/3 = 8 where the tangent lines have slope –1.

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Q: 9. Find the equation of the tangent line at point (2,2) on the curve fx) = x²- 7x + 12.

A: To find the equation of the tangent line

Q: ** 2 4. At every point of a certain curve, y=x²-. Find the equation of the curve if it is tangent to…

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Q: Find the x and y coordinates on the graph of f (x) = x³ - 3x where the tangent is horizontal. (A)…

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Q: At what point(s) does the curve y=; 3x – 4 have a derivative of -1? O 1) (2.0) 2) (-1,-7) 3)…

A: Given query is to find the value of x where seri is -1.

Q: The line normal to the graph of f at the point (1,2) passes through the point (-1,1).  Which of the…

A: Topic = Functions