An equation of the line tangent to the graph of f(x) = -x(1 – 2x)³ at the point (1,1) is a. y = -7x + 6 b. у %3D —6х + 5 с. у %3D —2х +1 d. y %3D 2х — 3 е. у%3D7х — 6 = -

Q: Find the equation of the line tangent to the graph of y = 4x (x - 4x + 5) at the point (2,8). y =

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Q: Show that the x-coordinate of the vertex of the parabola whose equation is y = ax2 + bx + c occurs…

A: Given the equation of a parabola y=ax2+bx+c

Q: Find an equation of the tangent line to the graph 16x4 + y4 = 32 at the point (1,2). %3D 1) 5 1 -+x-…

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Q: Find the slope of the line tangent to the graph of x^2+2xy^2+3y=31 at the point(2,-3)

A: The slope of the tangent line can be calculated by using the derivative of the function at the point…

Q: Find an equation of the secant line containing (1, f(1)) and (2, f(2)). f(x) = x² - 2x

A: Rule:-equation of line passing thraught (x1,y1) and (x2,y2) is y-y1=y2-y1x2-x1(x-x1)

Q: Find an equation for the line tangent to the graph of 7x f(x) = x + 7 at the point (3, 2.1). y =

A: Given curve is Differentiating with respect to x, we get

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

A: y=x3+2x   x1,y1 =1,3dydx=3x2+2slope of tangent at point1,3dydx1,3=312+2 = 5Slope of the tangent m =…

Q: The equation of the line tangent to the curve y=3x+4/4x-3 at the point (1,7) is  a) y - 25x=-18 b) y…

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Q: Find an equation of the curve that passes through the point (0, -7) and whose slope at the point 2x…

A: we have to find the equation of the curve

Q: 4) Find an equation of the line tangent to the graph of 2x³y³ = 2y – 4x at the point (-1, –1). Show…

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Q: Find the slope of the curve x²+y²-6x+10y÷5=0 at point (1, 0)

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Q: The slope of the curve y- xy- 3x = 1 at the point (0, -1) is а. 1 с. -1 b. 2 d. -2

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Q: Find the equation of a tangent line to the curve y= 2x3 - 3x2 - 10x +1 which is perpendicular to the…

A: Explanation: Given that,  y=2x3-3x2-10x+1     Concept Used: 1. Slope of the tangent is the first…

Q: 2.) What is the equation of the line tangent to y(x) x- 2r3+6x-3 at r =-1?

A: Follow the steps .

Q: Find the slope of the curve at the given point: y = x(4x − 1)², (1, ²) -

A: Given query is to find the slope of the curve at given point.

Q: Find the equation of the curve that passes through the point (0, 2) and has a slope of at any point…

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Q: Find the equation of the line tangent to y = x2 - 1 going through x = 1

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Q: What is the slope of the tangent line to the graph of any quadratic function of the form y=ax²+bx+c…

A: First find the vertex of the parabola, y=ax2+bx+c . Then, compute the expression for dydx .…

Q: _1. What is the slope of the tangent line to the curve y = 3x² – 5 at point (-1,-2)? a. -5 b. -6…

A: Using Derivatives & Application of derivatives

Q: 9. Find the equation of the line tangent to the curve y = 3x5 + 10x³ + 15x + 1 at its point of…

A: the given curve , y=3x5+10x3+15x+1 we have to find the equation of the tangent line to the given…

Q: Find an equation of the curve that passes through the point (0, 2), and has the given slope y′ =…

A: y'=x4y, (0,2) Formula ∫xndx=xn+1n+1+C

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

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Q: Determine the equation of the tangent to the graph of y- x - 3x + x+3 at the point (- 1, -2). O a)…

A: We have to find the tangent of the given function at point (-1,-2).

Q: 25. Find the equation of the line tangent to the curve x2 + y2 = 1 through the point (,).

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Q: 6. Find an equation in the form y = ax³ + bx² + cx + d__whose graph has an x-intercept at x = -1, a…

A: Given: x-intercept at  y = 2 y-intercept at x = -1 slope at (-2,-2) is 5. (-2,-2) lies on the curve…

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

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Q: (3) Find an equation of the tangent line to the curve y = 2x² + 3 that is parallel to the line %3D…

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Q: The line y=3x+6 is tangent to the graph of y = (-48)/(x-6) at the point ?

A: The given equation of tangent is y=3x+6 and its tangent to graph of y=-48x-6. To find the points at…

Q: Find an equation of the curve that passes through the point (0,1) and whose slope at (x, y) is 11xy

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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: Find an equation of the tangent line to the graph of y = 2x² + 3 that is parallel to the line 8x - y…

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Q: 9. Find an equation of the line tangent to the curve y = 2x - 7x2 + 10 at the point (3, 1). y = 12

A: Given that, the curve is y = 2x2 - 7x2 + 10  To find the tangent line to curve at point (3,1)   To…

Q: Find the equation of the line tangent to the graph of f(x) = 5x° +4x² – 5z – 6 at z = -6. %3D

A: Given that       f(x) = 5x3+4x2-5x-6      at x=-6 Here we have to find the equation of the line…

Q: Find the equation of the line tangent to x^2 + y^2 - 6x + 2y = 0 at (0,0)

A: Implicit Differentiation In implicit differentiation, when we differentiate y, we use y' or dy/dx…

Q: The line whose slope is 3 is tangent to the curve y=x² + 3x + 2 at the point, O (3,-2) O (-3,2) O…

A: The line whose slope is -3 is tangent to the curve y=x2 +3x+2 at the point. Here slope and line…

Q: 3.Find the coordinates of the points on the curves y =x3 -3x2-12x+10 with the gradients -2.

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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…

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

Q: The equation of the line with gradient 4 which passes through the point (1,2) is: O y = 2x – 4 y =…

A: Equation of line can be taken as y=mx+c

Q: Find an equation of the curve that passes through thepoint (0, 1)and whose slope at (x, y) is xy.

A: To Determine: Find an equation of the curve that passes through the point (0, 1)and whose slope at…

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: Find an equation of the line tangent to the curve defined by x^3+6xy+y^5=21 at the point (2,1)

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Q: A heat-seeking particle is located at the point (2,3) on a flat metal plate whose temperature at a…

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Q: ]Find the x-intercept of the curve that passes through the point (0,2) and whose slope at (x,y) is…

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Q: The cubic function y = ax3 + bx2 + cx +d pass through (0, -6), (1, -2) and tangent to the line 3x -…

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Q: Find the slope-intercept equation of the line tangent to the graph of y = 2lnx when x = 5. 2 -x-…

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Q: Find the equation of the tangent line to the graph og 8y^3-4xy^2=20 at the point (-3,1)

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Q: What is the equation of the curve passing through the (1, 16) and having a slope at any point (x,y)…

A: Given- 2xyx2+3 To find- The equation the curve passing though the (1,16) and slope at any point x,y…

Q: 4) Find the slope of the curve y = 3x + 1 at point P (1,2)

A: We need to find slope of curve at given point.