Show that, for any cubic function of the form y = ax + bx² + cx + d, %3D there is a single point of inflection, and the slope of the curve at that point b? За" is c -

Q: At what point of the parabola is the tangent line parallel to 7x+y-2=0? y=2x^2-3x+1

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Q: Find the tangent to the parabola (x + 2y)² + 2x - y - 3 = 0, parallel to the line x - y = 1.

A: Consider the equation of the line x-y=1 ⇒y=x -1 Comparing with y=mx+c we get slope of line, m=1

Q: Show that the square of the length of subtangent at any point on the curve by2=(x+a)2 (b is not…

A: Here given curve  by2=x+a2

Q: The slope of the tangent line to the parabola 2x + 4x + 5 at the point (3, 35) is: The equation of…

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Q: Find an equation of the tangent line to the parabola y = x2 -1 at the point (2,3) y 4x-5 Oy - 4x - 9…

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Q: (a) Find all the points on the graph of (x² + y? + y)2 x² + y? that have horizontal tangent line.

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

Q: show that the square of the length of subtangent at any point on the curve by2=(x+a)3(b is not equal…

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Q: The cubic y = ax3 + bx? + cx + d tangent to the line y = 12x + 13 at (-1, 1) and have a horizontal…

A: Solution...

Q: Find the parabola y= ax2+bx+c that passes through (2,1) and be tangent to the line y=2x + 4 at (1,6)

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Q: The tangent of the parabola x = y² + y + 1 at the point (1,0) is

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Q: Find the length of the curve y x² Inx 8 at (2 <x< 4)? -

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Q: The slope of the tangent line to the parabola y= 4x2 + 2x + 4 at the point (-1, 6) is : ?  the…

A: Consider the equation of the parabola, y=4x2+2x+4 The first derivative dydx of the curve at any…

Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y x2 for -2 < x<…

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Q: 4. Determine the slope of the common tangent to the parabolas y=x² +1 and y=-x² - 1. y=x*2+1 (a, b)…

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Q: The slope of the tangent line to the graph of the function y = 9Va -2 at (4, 16) is -5.00 O -4.00 O…

A: Simply calculate the derivative of function at given point.

Q: When we are standing at the point (1,-3), the function f(x, y) = 3x²y+xy is increasing most rapidly…

A: We have to find the direction of  rapid increase of the function using gradient of the function.

Q: What can you say about the inflection points of a cubic curve y = ax3 + bx2 + cx + d, a ≠ 0? Give…

A: To find the point of inflection, we find the values of x for which the second derivative of the…

Q: Find the set on which the curve 7 dt t2 + 6t + 15 y = is concave downward. Answer (in interval…

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Q: I dont know where to start this problem. It would be great to have some help

A: Given:

Q: Show that the square of the length of the subtangent at any point on the curve by2=(x+a)3 (b is not…

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Q: Find point on the ellipse x^2+2y^2=1  where the tangent line has a slope of 1.

A: We know, slope of tangent line = dydx

Q: 4. What is the area of the largest rectangle that can be insribed in the first quadrant under the…

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Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the…

A: Given" Parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at…

Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0,1) and is tangent to the…

A: Since, the parabola passes through (0,1) ,so,we substitute x=0, y=1 ,to get c=1

Q: Find the point (xo, yo) on the graph of y = x³ + 3x? + 8x – 3, at which the slope of the tangent…

A: To find the slope of the function we need y'y=x3+3x2+8x-3y'=3x2+6x+8

Q: The slope of the tangent line to the graph of the function y = 8Vx – 3 at (9, 21) is %3D 1.33 -2.33…

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Q: Give the equation of the tangent which passes through the point with the coordinate x=2 of the…

A: Equation of tangent problem.....

Q: a) Determine the point at which the slope of the tangent to each parabola is zero. i) y= 6x2-3x + 4…

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Q: Find the slope of the tangent to a parabola y=x^3 at a point on the curve where x=2

A: Consider the following equation:

Q: find the length of the curve 3y2=4x3 from x=0 to x=8 when y greater than or equal to 0.

A: The formula for length of a curve f(x) extending from point a to point b is given as,

Q: Determine the points where the curve f(x) = 2x3 + 3x2 – 36x + 1 has a horizontal tangent. -

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Q: The line y = 2x - 9 is tangent to the parabola y = x'2 + ax + b at the point (4,-1). What are the…

A: Given y=2x-9 is tangent to y=x2+ax+b at (4,-1) So, y=x2+ax+b passes through (4,-1)Put x=4 and…

Q: A particle travels along the parabola y = ax^2 + x + b. At what point do its abscissa and ordinate…

A: Given: y=ax2+x+b

Q: The slope of the tangent line to the parabola y 4x? + 7x + 3 at the point (0, 3) is: The equation of…

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Q: Find a cubic function  y = ax3 + bx2 + cx + d  whose graph has horizontal tangents at the points…

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Q: The slope of the tangent line to the parabola y 3x? + 2x + 3 at the point (– 5, 68) is: The equation…

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Q: Find x for which the line tangent to the parabola y = 4x − x^2 is horizontal

A: The objective is to find x for which the line tangent to the parabola y = 4x − x^2 is horizontal.

Q: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for -1 <x<…

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Q: What is the maximum vertical distance between the y=x+2 and the parabola y=x^2 for -1 is less than…

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Q: What is the equation of tangent to the parabola y^2 = 2x + 8 at (4,4) ?

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Q: What is the smallest possible area of the triangle that is cutoff by the first quadrant and whose…

A: Given that the triangle that is cut off by the first quadrant and whose hypotenuse is tangent tothe…

Q: Show that the square of the length of subtangent at any point on the curve by =(x+a)°.(b÷0) varies…

A: We will prove it as following.

Q: Determine the co-ordinates of all the points at which the tangent to the curve y = 3x'e8x is…

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Q: Suppose that/ (3r-x²) dr=Ax'+Bx'+C, for constants A, B, C. What is the value of C if the curve =…

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: Find a parabola with equction Y=ax +bx+c that has a Slope I at x -1, slope 9 at x=-1, and passes…

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Q: Two different level curves of the graph of z = f(x, y) can intersect. True False

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Q: Find a cubic function y = ax3 + bx2 + Cx + d whose graph has horizontal tangents at the points (-2,…

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Q: Find an equation of the parabola y = ax² + bx + c that passes through (0, 1) and is tangent to the…

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Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y = x< for -2 <x<…

A: To Find