6. Find an equation in the form y = ax³ + bx² + cx + d__whose graph has an x-intercept at x = -1, a y-intercept at y = 2 , and a tangent line with slope of 5 at (-2, –2).

Q: 19. Does the line that is tangent to the curve y = x3 at the point (1, 1) intersect the curve at any…

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Q: 5. Find the equation of the tangent line that passes through point (1,2) to the graph 8y3 + x²y – x…

A: Proceed as shown below...

Q: Find the equation of a line normal to the graph of y = 3x+5/x−1 at x = 3

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Q: 5. Find the equations of the tangent line and normal line to the parabola y = 2x² at the point…

A: Since, you have asked multiple questions , according to our guidelines we are supposed to answer…

Q: 2 Find the line tangent to the curve r3 +y3 at the point 4 (-3/3, –1).

A:

Q: Find the points on the graph of y = 1– 5x + 3x² where that tangent line is parallel to the line y –…

A:

Q: Find an equation of the tangent line to the graph at the given point. 3(x² + y2}² = 100(x? – y²),…

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Q: 5. Find the equation of the tangent lines to the curve y = x² + 3x -4 and parallel to the line 6x…

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Q: B. Find the slope and the equation of the tangent line to the curve 1. y = 4 - 3x at (- 1, 1) 2. y…

A: We need to find the slope and the equation of the tangent line tothe following curve:3. y=3x2+2 at…

Q: Find the slope of the tangent line that passes through point (1, 2) to the graph 8y³ + x²y O-2/97…

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Q: 3. Find the slope of the graph tangent to the curve y =x* - 2x3 +x that passes through the point (2,…

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Q: Find the equation of the tangent line to the graph of x4y16=1 at the point (81,1/3) and at the…

A: We use slope point form to equation of tangent line.

Q: 10. Find the slope-intercept form of the equation of the line tangent to the graph of y arctan(9x)…

A: Given y = arc tan9xand x=39here we find the slope - intercept form of the equation of the line…

Q: Find the equation of the tangent line to the graph of y = 2x - (4 / √x) at the point (4, 6).

A: Given,            y = 2x - 4x and Point is 4, 6

Q: Find an equation of the tangent line to the graph of Y = e2x-3 at the point (3/2,1).

A:

Q: 1) Find the slope of the tangent lines on the curve y = 6x + 24x -39x - 43 at points | (-5,2) and…

A: Slope of line is given by m = dy/dx = tan θ y = 6x3 + 24x2 - 39x - 43  Differentiating with respect…

Q: 13) Find the equation in slope-intercept form that is tangent to (x- 1)² + (y + 2)² = 25 and passes…

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Q: Show that no point on the graph of x 2 - 3xy + y 2 = 1 has a horizontal tangent line.

A: Given  x 2 - 3xy + y 2 = 1

Q: 5) What is the equation of the line tangent to y = 2x³ + 3x - 1 atx=0?

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Q: 2. Find the equation of the tangent line (in slope-intercept form) to the curve y=xvx that is…

A:

Q: Find an equation in the form y = ax² + bx + c_whose graph has an x-intercept at x = -1 and a tangent…

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Q: 8. Find the point on the graph y = x³ where the tangent line is perpendicular to the line 3x +9y = 4

A: We have to find the point where tangent line is perpendicular to the line 3x+9y=4.

Q: 2. Find the slope of the tangent to the curve y = 3 + 4x² - 2x³ at the point where x = a

A: given,y=3+4x2-2x3

Q: 7. Find the slope of the line tangent to the curve at the point (2,1). x²y + xy² = 3x %3D

A: 7. The equation is given by x2y+xy2 = 3x                                                ......(1)…

Q: Find all the points on the graph of (x² + y²)² = x² – y² that have vertical tangent line.

A: This question is taken from the tangent and line in which we have to all points on the graph that…

Q: 1. What is the slope of the tangent line to the curve 4x2 - 9y² = 1 at point (3,2) ? b. - 27 8 a. 3…

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Q: 11. What is the slope of the tangent line to the curve y = 3x2 - 5 at point (-1,-2)? а. -5 b. -6…

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Q: 2. Find the slope of the tangent to the curve y = 3 + 4x² − 2x³ at the point where x = a -

A: The equation of the curve is given by y = 3+4x2-2x3 To evaluate: The slope of the tangent to the…

Q: 2. Write the equation of the tangent line to the curve y = x3 – 6x at the point (2, –4).

A:

Q: What is the equation of the line tangent to the graph of y = (2x+3)/(3x-2) at the point (1,5)? 13x -…

A:

Q: 7. Find the slope of the tangent line to the graph at (1,1): x2y? - 9x2-4y2 = 0 x-9-4-0 (-4, 2/3)…

A: x2y2−9x2−4y2=0 Use implicit differentiation to find the slope of x2y2−9x2−4y2=0 Implicit…

Q: 4. Find the equation for the line tangent to (persamaan garis şinggung) a. y= x2- 3 x + 5 at the…

A: The objective of the question is determine the equation of the tangent line.

Q: 1 Find an equation of the line tangent to y at point (0, -). X-3

A: Given y=1x-3 at point 0,-13 To find equation of line tangent:

Q: 7. Find the member of the curve whose slope at any point is 2e¹x and passes through the point (0, 1)

A:

Q: 1 - Find the equation of the tangent line to the curve y = 3 5 x2 +6x 2 11 at its point of…

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Q: 4. The slope of the tangent line to the curve y 4. is: 9 - at the point 9, The equation of this…

A: To find the slope of the tangent line to the curve, y=4x, at the point 9, 49.The  equation of this…

Q: Find an equation of the tangent line to the graph of y = x³ - 3x - 1 at the point (2, 1).

A:

Q: 5. Find the point on the parabola y=-x+3x+4 where the slope of the tangent line is 5.

A:

Q: Show that the curve y =6x3 +5x -3 has no tangentline with slope 4.

A: Consider the following equation of curve: y=6x3+5x-3 Differentiate y with respect to x:…

Q: 4. Find the equation of a curve whose slope at any point is equal to x + + and which passes through…

A:

Q: At what point (x,y) is the tangent line to the curve y=2x2-5x+8 parallel to the line y=3x-7

A: It is given that

Q: Show that the curve y = 6 x 3 + 5x -3            has no tangent line with slope 4.

A: y=6x3+5x-3 has no tangent line with slope 4

Q: 9. Find the point on the graph of y = x² where the tangent line is parallel to the line 3x – 4y = 4.

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Q: 2. Determine the equation of the line tangent to the graph of y = x³ + 2x at the point (1,3).

A:

Q: 2. Find an equation of a curve satisfying the ff. condition and passing through the point (0, -1).

A: dxy-dy1+x3=0A first order separable ODE has the form of Ny·y'=MxLet y be the dependent variable.…

Q: At what point on the graph of y = (x^2)/2 is the tangent line parallel to the line 2x - 4y = 3? O…

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Q: 1) Find the slope of the line tangent to the graph of y=x²+1at(2, 5).

A:

Q: 2. Find the curve that passes through the point (1, 3) and whose tangent line at (x, y) has slope

A: Solve for the curve

Q: 4. Find the member of the curve whose slope at any point is 4y point (3, 4) and passes through the

A: Note: As they are different questions, as per our company guidelines we are supposed to answer the…