Find the point on the graph of f(x) = Vx that is closest to the point (8, 0). (х, у) -

Q: Find the equation of the tangent and normal line of the function f(x) = 2x – 1 at the point (5, 3).

A: fx=2x-1   First find equation of tangent line of given function  We need to find the slope of…

Q: Find the equation of the tangent and normal line of the function f(x) = V2x – 1 at the point (5, 3).

A: fx = 2x-1     , 5,3f'x = ddx2x-1     = ddx2x-112        = 122x-1ddx2x-1        = 222x-1 = 12x-1∴f'5…

Q: Find all points (x, y) on the graph of f(x) = x - 3x + 8x + 23 with tangent lines parallel to the…

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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 the point on the line y = 3x + 4 that is closest to the origin. (x, y) = |

A: To find - Point on the given line closest to the origin.

Q: The equation of the line tangent to f(x) = (x² – 9) (2x – 1) at æ = 2 is y = 2x –*

A: Given that: f(x)=(x2-9)(2x-1)

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: The slope of the curve 2x + Vx + y = y at the point (0, 1) is

A: 2x + √(x+y) = y  So,  √(x+y) = y - 2x So, x+y = (y-2x)² So, x+y = y² + 4x² - 4xy  So, y(1+4x) - y² =…

Q: Find an equation for the line tangent to the graph of  f(x)= 2xex at the point (3,f(3)). y=?

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Q: The point on the curve y=vx+2 which is closest to the point (5,2) is

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Q: Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y-2y³ In the…

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Q: Find an equation of the line tangent to the graph of the function: f(x) = V2x² – 1 at point P(-1;1).

A: Given:- f(x) = (2x2-1)(1/3)  To find:- Equation of tangent line at point p(-1, 1) on given curve

Q: Find all points (x, y) on the graph of f(x) = x° - 4x + 20x + 11 with tangent lines parallel to the…

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Q: Find the equation of the tangent line to the graph of x^2 * y^2 + 6xy =1512 at the point (-7,6)

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Q: Find the point on the line y = 2x + 3 that is closest to the origin. (x, y) =

A: The perpendicular drawn from the origin to the line represents the shortest distance.

Q: Find the point (x0, yo) on the graph of y = x + 9x² + 8x – 5, at which the slope of the tangent line…

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Q: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

A: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

Q: find all points (x,y) on the graph of f(x)=3x^2-5x with tangent lines parallel to the line y=7x+1.

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Q: Find the slope and equation of the line tangent to f (x) = x2 +9 at the point (1, 10).

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Q: 2xy - y² + x = 2 at the point (1,2). - Find the equation of the tangent line to ² +2

A: By using equation of tangent line formula, we find the required tangent line.

Q: Find the point on the line y = 4x + 3 that is closest to the origin. (x, y) =

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Q: Find the point on the line y = 3x + 4 that is closest to the origin. (x,y)=

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Q: The derivative of the function y = tan(In(vx² – 6x + 1)) is: %3D

A: Formula:ddx(tan x) = sec2xddx(ln x) =1xddx(xn) =n xn-1

Q: Find the derivative using the long method 3 u = t2

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Q: find an equation of a straight line tangent to the curve y=e^x and passing (0,0).

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Q: Find the equation of tangent and vertical line to the curve g=x+1/x at point (0,1)

A: First we want to check whether the given point is in the domain of the given function.

Q: What is the gradient of the curve y = x^3+4x^2-6x+3   at the point where x=-2 ?

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Q: Find the equation of the line tangent to the graph f(x) = – at the point (4,1).

A: Given:            fx=4x To find the slope of the tangent line, find the value of the derivative of…

Q: Find the point on the line y 2 x-3 that is nearest to tne ofigin.

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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 gradient of the curve . Y=4x^2 at x=3

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Q: Find the slope of the line tangent to y = 3x(cos x) at (7/2, 7/2). A) -3/2 B) 3x/2 C) /2 D) -x/2

A: Consider the function  y=3x(cosx) Point : π2,π2

Q: Find a point on the graph where x = t² - 1, y = 2t has a vertical tangent.

A: For vertical tangents dx/dy=0

Q: Find all points (x, y) on the graph of f(x) = x° - 5x + 26x + 19 with tangent lines parallel to the…

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Q: The slope of the line tangent to the curve y = x*- 8x3 + 22x² – 24x + 9 at x = 1 is _.

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. (x, y)…

A: First find gradient and take magnitude for max rate of change

Q: Find all points ( x,y) on the graph of f(x) = 3 x² – 4x with tangent lines parallel to the line y=…

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Q: Determine an equation of the tangent line to y = (e3x - 2)4  at the point (0,1) then solve for y.

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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: Find the derivative of the function. f(z) 0.6z-0.4z2 - 0.8 f' (z) -

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Q: Find the equation of the tangent line to f(x)=4x+x^−1/2+1 at the point (4,35/2)

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Q: Find the derivative of the fünction. y = 7(6 - x2)6 %3D

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Q: What is the equation of the tangent line to the curve f(x)= 4x2 + 2x -1 at the point x=0 ?  a.)…

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Q: Find the derivative, or y', of ³ – Vy = ¿y² + 6 at (2,1).

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Q: Find the equation of the line tangent to f(x)=3/(2x+1)at the point (1, f(1))

A: Given function is  fx=32x+1

Q: Find the equation of the line tangent of f(x) = 3x - e-5x when x = 0.

A: f'x=3-e-5x-5=3+5e-5x We know that the slope of the tangent at x=a is f'(a). So the slope of the…

Q: Find the derivative of f(z)=((11z+4)1/2)(e3z).

A: Given function f(z)=11z+412e3z

Q: Find y" by implicit differentiation. 9x2 + y2 = 4 y" = %3D

A: