1) Y= DCY, i-s, )+G+ E, (IS equation) a) write i as an impliat function of the otner variables in the IS equation

Q: Find all points (x, y) on the graph of g(x) = x3/3 -3x2/2+1 tangent lines parallel to the line 8x -…

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Q: What are the coordinates of the points in the graph of y² –x²+ 6x – 13=0 in which the tangent line…

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Q: If the line y=x+4 is tangent to f(x)=ax2 +bx at the point (2,6), then a+b?

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Q: The tangent line equation of 2x6+y4=9xy at the point (1, 2) is ….

A: The tangent line equation of 2x6+y4=9xy

Q: Find equations of the two tangent lines to the graph of f(x) = 2x2 that pass through the point (-1,…

A: Here, the given curve is: f(x)=2x2 To find two tangent lines that pass through (-1,-6)

Q: Show that u = 3x^2y + 2x^2 - y^3- 2y^2 is a harmonic function.

A: Given: u=3x2y+2x2-y3-2y2 To show: u is a harmonic function.

Q: 9. What is the equation of the line tangent to the graph of the function f at the point (1,1)? f (x)…

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Q: 5 Find the equations to both lines through the point (2,-2) that are tangent to the parabola y = x²…

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Q: The tangent line equation of 2x6+y4=9xy at the point (1, 2) is ... ....E Persamaan garis singung…

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Q: 21. Let Sech u = 3/5 , determine the values of the remaining five hyperbolic functions.

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Q: The slope of the tangent line to the parabola y 2x + 3x +6 at the point (1, 11) is: The equation of…

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Q: Find an equation of the tangent plane to the graph of f(x, y) = xy3 + x2at (2, -2, f (2, -2)).

A: fx, y=xy3+x2 Partially differentiating with respect to x, keeping y as constant, we get fxx,…

Q: Find an equation of the tangent line at the given point. (x + 2)2 − 6(2y + 3)2 = 3, (1,−1)

A: Consider (x + 2)2 − 6(2y + 3)2 = 3, (1,−1)

Q: Find the equation of the tangent line to f(x)=−2x−4x^−1/2+3 at the point (4,−7).

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Q: What are the coordinates of the points in the graph of y2-x²+6x – 13=0 in which the tangent line is…

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Q: find an equation of the tangent line f(x)=x+(6/x)    points (x,y)= (-6,-7)

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Q: Determine the equation of the tangent line of the given function: f(x) = 3x² – 2x; (-1,5) y = -8x-3…

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Q: Find the point (s) on x = 3 - y2 that are closest to point A = (1,0).

A: Given: x = 3 - y2 and point A = (1, 0)

Q: 17. Passes through the point (2, 1) and is perpendicular to y = -x+ 3.

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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: Show that no point on the graph of x 2 - 3xy + y 2 = 1 has a horizontal tangent line.

A: Given  x 2 - 3xy + y 2 = 1

Q: What are the coordinates of the points in the graph of y2-x²+6x – 13=0 in which the tangent line is…

A: To find the points at which tangent line is horizontal , y' =0.

Q: Find the equation of the tangent line at (2, f(2)) when f(2) = 9 and f'(2) = 3. |3D

A: GIVEN FOR A FUNCTION f(x) ,f(2) = 9            &  f'(2)=3

Q: Find equations of the two tangent lines to the graph of f(x) = x- that pass through the point (-1,…

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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 all the points on the graph of (x² + y²)² = x² – y² that have vertical tangent line.

A: This question is taken from the tangent and line in which we have to all points on the graph that…

Q: If the tangent line to y f(x) at the point (1,2), passes through the point (-1,1), then f'(1) = %3D…

A: Find f'(1)

Q: Let (21, Y1) = (7,9), m = 3. Then the equation of the tangent line is O y = 3x- 20 O y = 3r - 16 O y…

A: Equation of the tangent line = ?

Q: Write down an equation of the tangent line to the graph of 2x-3 f(x) = at a= – 1 %3D X+4 y 11 y= 6.…

A: Topic: function and derivatives

Q: What are the coordinates of the points in the graph of y2 – x² + 6x – 13= 0 in which the tangent…

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Q: Differentiate the given function glu)- In (u+ Vuzti)

A: Differentiate using basic laws

Q: Find equations of the two tangent lines to the graph of f(x) = x² that pass through the point (-1,…

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Q: Find equations of the two tangent lines to the graph of f(x) = x2 that pass through the point (-1,…

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Q: What are the coordinates of the points in the graph of y² – x² + 6x – 13 = 0 in which the tangent…

A: As we know that; The slope of the horizontal tangent line is zero or m=dydxPx0,y0=0 Given;…

Q: Write an equation for the tangent line to g(x) at x = 2 if g(2) = 7 and gʻ(2) = –3.

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Q: What are the coordinates of the points in the graph of y-x+6x – 13=0 in which the tangent line is…

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Q: (a) Find the equation of the tangent plane to the graph of : = (1,-1,5). + ) +4 at

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Q: Find the tangent of ZU. V11 12 U V

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Q: slope of the tangent to the curve y2x+ y2x2 =6at (2,1) is

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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: 2x + 2 and the tangents to it at (1, 2 1 and 2 (4, 2) is

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Q: What are the coordinates of the point on the graph of Ax) = (x+ 1)(x+ 2) at which the tangent is…

A: solution:-f(x)=x+1x+2      =x2+3x+2slope of tangent=ddxf(x)                             =ddxx2+3x+2…

Q: 22. If the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f'(4).…

A: #22 f(4) ? f'(4)?

Q: Find equations of the two tangent lines to the graph of f that pass through the indicated point.…

A: Given function is fx=4x-x2. To find the equations of the two tangent lines to the graph of function…

Q: Find an equation of the tangent line at the given point. 2x1/2 + 4y −1/2 = xy, (1, 4)

A: Given,

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: