Which of the following is the equation of a line tangent to the graph of f(x) = x* + 1 and parallel to the line y = 32x – 2? %3D - 16х — у 3 39 y = 32x + 39 O y + 47 = 32x 32x – y + 47 = 0

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

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Q: 4. Find the equation for the line tangent to a. y=x²- 3 x + 5 at the point (2, 3)

A: We will find tangent equation.

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

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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: sketch the shifted exponential curves y = 3x + 2 and y = 3-x + 2

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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 the slope and equation of the line tangent to f (x) = x² – 4 at the point (3, 5).

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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: 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: 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: Parallel to x + 2y = 0; (1, 2) on line

A: To find the equation of line paralley to x+2y=0 and (1,2) is on the required line.

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: Find an equation of the line tangent to thegraph of ƒ(x) = x3 + 4x at (1, 5).

A: Given: The graph is expressed as fx=x3+4x To Find : Equation of line tangent to 1,5  The equation of…

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: Does the given equation define an implicit function around the point (y=3, x=1) and why?

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Q: Find the equation of the curve that passes through the point (6, 6) if its slope is given by dy = 7x…

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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 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 (3, 2) if its slope is given by y = dy…

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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: Find the equation of the curve that passes through the point (8, 6) if its slope is given by dy = 5x…

A: Given that, the curve passes through the point 8,6 and the slope is given by dydx=5x-7

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: 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: 4. Find the equation for the line tangent to a. y= x²- 3 x + 5 at the point (2, 3)

A:

Q: Find the equation of the curve that passes through the point (8,2) if its slope is given by…

A:

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

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

Q: Find the slope of the curve at the point (2,3) * x³ 2x + 1 3/2 1 O 1/2 O 1/4

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Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 36x2 +…

A: for horizontal tangent,  dy/dx =0

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: Show that the equation y^2=x determines an infinite number of implicit functions.

A: Consider the given equation: y2=xSolve in terms of y:y=±xSo, there are two functions that can be…

Q: Find the equation of the curve that passes through the point (5,4) if its slope is given by…

A: dydx=5x-2dy=5x-2dxIntegrate on both sides

Q: Find the equation of the line tangent to the graph of f(x)= 7x³ +5z2 - 3z- 3 at z = -5. %3D

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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: -4 The number of tangents to the curve of y=- x³ + 6x? which have a slope of 8 is:

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Q: Find an equation of the curve that passes through the point (8, 2), and has the given slope y′ =…

A: Solution:-We have to find an equation of the curve that passes through  the point (8,2) and having…

Q: The slope of the tangent line to the graph of the function y = 8Vx - 2 at (4, 14) is . O-3.50 O2…

A: We will find the derivative of the function y and evaluate it at x = 4 to find the slope of the…

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: 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: ]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: What is the slope of the tangent line to the graph of the solution of y' = 3√√y + 7x³ that passes…

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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 curve that passes through the point (6,6) if its slope is given by dy/dx =…

A:

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…