The slope-intercept form of the line with soope equal to 2/9 and y-intercept at (0,4) is

Q: Find the equation of the tangent and normal line of the function y^3 +3xy + x^4 = 5 at the point (1,…

A: y3+3xy+x4=5 Differentiating with respect to x, we get…

Q: A curve on the xy-plane passes through the point (0, a) for some number a, and has the property that…

A: This problem is based on a variable separable first order ordinary differential equation. We have to…

Q: 2 Find an equation of the line L, where L is perpendicular to y =x and passes through the point…

A: Given a Line L which is perpendicular to  y = (2/3)x  at point (3,2)  Equation of line L is…

Q: Find the equation of the curve that passes through the point (1, 3) and has a slope of at any point…

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Q: 1. Circles through the origin with centers cn the x-axis 2. Straight lines with slope and…

A: First of it requires basic formula for circle and straight line. Then we will apply the given…

Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 5  where the tangent line is horizontal. (x,…

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Q: The graph of f(z) = 2z³ + 12z² – 126z + 17 has two horizontal tangents. One occurs at a negative…

A: for the horizontal line find the slope first and set to zero.

Q: 2. Find the slope of the tangent line to the curve y = 4x² – 2 at x= 1. What is the equation of the…

A: The given curve is y=4x2-2. At x=1, y=412-2=2. Thus, the graph is passing through 1, 2. The slope of…

Q: 12. Determine the y-intercept of a line with a slope of -2 that is a tangent to the curve: y =…

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Q: 3. Find the tangent lines and normal lines to the curve y = x4 - 4x3 + 6x2 – 4x + 3 with slope…

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Q: Where on the curve y = (256 + x²) * does the have the greatest slope? %3D NOTE: Enter the exact…

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Q: 15. Find the equation of the curve whose slope at any point is equal to -(y +1)/(x + 1) and which…

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Q: Q3: Find equations of all lines having slope (-1) that are tangent to the curve y = 1/(1-x)

A: y=11-x Also, the given Slope is -1

Q: The curve for which y'' = 6 has a slope of –3 at its point of inflection (2, 3). Find the value of y…

A: y''' = 6 Implies, y" = 6x + a, where, a is a constant. &, y' = 3x² + ax + b, where, b is a…

Q: Find the point on the graph of y = x3 such that the tangent at the point is parallel to the line y –…

A: Consider a graph: y=x3……1   Equation of line parallel to the tangent of above equation is:…

Q: tangent to the curve x^3 +x^2 y + 4y - 1 + 0 at the point (3,-2) has a slope equal to: a. -13/15…

A: We will find the slope.

Q: See image below

A: Given function is

Q: A line is tangent to y = x - 2 at (2,6). What is the coefficient of x when the line is in the form…

A: Given curve y=x3-2    ;   (2,6)

Q: The curve for which y'' = 6 has a slope of –3 at its point of inflection (2, 3). Find the value of…

A: Given that, y'''=6

Q: with a slope of 2. 48. Find the equation of the tangent and normal lines to the curve y x+x² – x+1…

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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: find the equation of the line tangent to the curve y=x^4-4x^3+2x^2-4x+15 and perpendicular to the…

A: To find the line tangent of the curve we have to differentiate with respect to x. If first-line…

Q: 2) Find the equation of the curve whose slope at any point p(x,y) is m =x (x +5)² and passing…

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Q: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangents…

A: To determine the x-intercept of the curve and slope of the tangent at the intercept.

Q: 4. Find the equation of the curve for which y""= 2x³. The slope of the inflectional tangent at (-1,…

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Q: 1. Find the DE of all straight lines with slope and y-intercept equal.

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Q: 8. Find the point on the curve y = √2x 3 from the point (1, 4)-

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Q: How fast does the  slope of the curve y= (x2+x+1)2 change at the point where x=2

A: First derivative of a function represents the change in function or slope of the function and second…

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 the slope of the curve: y= x^2/x^2 -1 at x=2

A: Slope of curve is the derivative of curve at the point .  Slope = m = ( dy/dx ) | x = a

Q: The curve y = f(x) has a y – intercept of 3. The tangent to this curve at the point (x, y) has an x…

A: Given that the curve y=f(x) has a y-intercept of 3.  That means y(0)=3. also given that the tangent…

Q: The line that is normal to the curve x + 3xy - 4y² = 0 at (3,3) intersects the curve at what other…

A: Given: x2+3xy-4y2=0 at (3,3)

Q: 7. Find an equation of the line tangent to the curve y = 3x² – 1 and perpendicular to the line x

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Q: 3. Find the slope of the curve of the function y = at the point P (2,-).

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Q: The slope of the curve y^2-xy-3x=1 at the point (0,-1)

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Q: The curve for which y" = 6 has a slope of -3 at its point %3| of inflection (2, 3). Find the value…

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Q: 4) Find an equation to the line tangent to y = 5 + |x – 2| at the coordinate (2, 5).

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Q: The slope of the tangent at a point (x0, y0) of x3 + y3−6x2y = 0, is indicated as 4x0y0 −…

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Q: Find the point(s) on the curve of y = 3x^4 − 4x^3 where the tangent line is parallel to the line…

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Q: The gradient of the tangent to the curve y=-3x³ + 4ax² - 5x + 4 at x = 1 is 2. The value of a is 2.…

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Q: The graph of y = f(x) passes through the point (9,4). Also, the line tangent to the graph at any…

A: Given: The graph of y=fx passes through the point 9, 4. Also the line tangent to the graph at any…

Q: 15. Find the equation of the curve whose slope at any point is equal to -(y + 1)/(x +1) and which…

A: We have to find the equation of line when given slope and passing through the point

Q: perpendicular to the line 2x+ 5y 7 nbR uation of the line (in slope-lntercept form), passing through…

A: Given:     Point: ( 2 , -3 )       Line : 2x + 5y = 7

Q: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangent…

A: To find the x-intercept we plug y=0

Q: At the two points where the curve x2 - xy + y2 = 36 crosses the x-axis, the tangents to the curve…

A: x2-xy+y2=36

Q: 49. Find the slope of the curve y = (2x2 - x+ 3)(x + x+1) at (1, 12).

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Q: Find the equation of a Tangent line to y = 2x2 – 5x – 1 that is parallel to line x + y –

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Q: A line that is normal to the curve x^2+3xy-4y^2=0 at (6,6) intersects the curve at what other point?

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Q: Find the condition that the line ax+by=1 may be normal to the curve an-1y

A: Given problem is : Find the condition that the line ax+by=1 may be normal to the curve an-1y=xn…

Q: A curve for which y" = x passes through the point (1, –1) with a slope of. Find the y-value of at x…

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