Determine the area of the triangle formed by the tangent to the graph of the function y=3-x2 drawn at the point (1,2)and the co-ordinate

Q: Find the tangent line to the function f (x) = x² – 4x + 5 at the point (3,2).

A: To find: The tangent line to function fx=x2-4x+5 at the point 3,2. Formula used: The slope of…

Q: Find the slope of the tangent line to the graph at the given point.

A: Slope of the tangent line is the derivative of the given function at the given point. So…

Q: Find the equation of the tangent line to the graph of f(x) = 2x² –In Vx at X = 1. %3D

A: First we differentiate to find the slope then use formula to find the equation

Q: Please show step-by-step solution!

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Q: The slope of the tangent line to the graph of f(x) D x2 at a = -1 is: %3D %3D

A: Given  equation of the graph  f(x) = xx2-x                        ...........(1) We have to find the…

Q: Find distance between point A(1,3) Perpenclicular on the line L: 2y =2 +X

A: Use the following formula: The perpendicular distance from the point A(x1,y1) to the line ax+by+c=0…

Q: Find the equation of the tangent plane to the graph of 5y f(x, y) = at the point (9, –1). (Use…

A: The equation of the tangent plane at point (x1, y1, z1) is z-z1=∂z∂x(x1, y1, z1)(x-x1)+∂z∂y(x1, y1,…

Q: Find an equation of the tangent line to f (x) = x² Vx4 – 12 at x = 2. - %3D

A: Explained below

Q: Find the êquation of the tangent line to the graph of fCx)= 2x-5 at the x+1. Point at which x30 (617

A: We have to find the slope of tangent first.

Q: Find the equation of the tangent plane to the graph of 9y f(x, y) = at the point (4, –-1). (Use…

A: The Equation of the tangent plane: - z0=(x0,y0) is a point in the domain of f, and defined by a…

Q: Find an equation of the tangent line to the parabola y=x2+x such that it passes through the point…

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Q: Find the slope of the tangent line to the graph at the given point.

A: Slope:  The slope of a line measures the steepness of the line. The slope is calculated by rise over…

Q: The slope of the tangent line to the graph of the function y = 8VI - 4 at (16, 28) is O 1.50 O -1.75…

A: Given function is, y=8x-4

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

A:

Q: Find the​ x-coordinates of all points on the curve y = (-x^2+4x−3)^3 with a horizontal tangent…

A: We know the slope of the tangent where it is horizontal is 0. we will need to find the derivative of…

Q: Find the equation of the tangent line to the graph of f(x)= 1 at the point (2,1). %3D X-1

A:

Q: Determine the point(s) at which the graph of -8x f(x) = 2х- 1 has a horizontal tangent. (х, у) %3D

A: Solution - The derivative of a function is 0 at a point where the tangent is horizontal. Let us…

Q: Find the tangent line of the function f(x) = - 4Vx at x = 4, and the point at which tangent %3D line…

A:

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 points on the curve y= x 4-6 x2 +4  where the tangent line is horizontal.

A: Find the points on the curve y=4x-6x2+4  where the tangent line is horizontal.

Q: Find an equation of the tangent plane to the graph of f(x, y) = In(4x² – 2y2) at the point (1, 1).

A: To Determine: FInd the equation of tangent plane to the graph of…

Q: Find the slope of the tangent line to the graph at the given point. (4 - x)y? = x3, (2, 2) Cissoid:

A:

Q: The slope of the tangent line to the graph of the function y = 7Vx – 3 at (9, 18) is - O 3 - 2.00 O…

A: Simply take the derivative of the function at that point.

Q: Determine the area of the triangle formed by the tangent to the graph of the function y=3−x2 drawn…

A:

Q: Find all points on the curve y = x3 + 2x2 -6x +5 where is the tangent is parallel to the line 2x + y…

A: The given curve y=x3+2x2-6x+5

Q: ) Find the equation of the tangent f (x) = 4x - 8/x at a = 16. %3D %3D

A: Given: fx=4x-8x at x=16 For finding equation of tangent at x=16, we need to find y-coordinate for…

Q: Find the slope of the tangent line to the graph at the given point. (x² + y²)² = 4x²y, (1, 1)

A:

Q: Find the slope of the tangent to a parabola y=x^3 at a point on the curve where x=2

A: Consider the following equation:

Q: Find the slope and equation of the tangent line to f(x) = 3 – 2x at a = 3 using th definition.

A:

Q: Find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis and a tangent…

A: We have to find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis…

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: Find the slope of the tangent line to the graph at the given point. (x² + y²)² = 4x²y, (1,1)

A: To find slope of tangent of a curve at a given point, we need to find differential at that point

Q: Find the slope of the tangent line to the parabola y= 2 +x−x^2 at the point (0,2).

A: Simply take the derivative of the given equation and substitute the given point.

Q: Find the equation in terms of x and y of the tangent line to the curve r= 4sin 5θ and θ =π/3.

A: Given: r=4sin5θ  and θ=π3

Q: Find all points on the curve y = x³ + 2x² - 6x + 5 where the tangent is parallel to the line 2x + y…

A:

Q: The slope of the tangent line to the graph of the function y = 7 x – 3 at (9, 18) is. O -2.67 O 1.17…

A: We know that dy/dx gives slope of tangent at any point.

Q: find the x-coordinates of the point on the curve y=2x^3-3x^2-36x-1 where the tangent is horizontal.…

A: For finding tangent is horizontal take slope 0

Q: Find the slope of the tangent line to the graph of the function at the point (1, 0). y 4 3 2 1 /1,0)…

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Q: Find the equation of the tangent line at the given point on the curve. 3y-x = 8, (16,2) %3D

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Q: Find the points on the graph of f(x) = 36x – 3x³ where the tangent line is horizontal. %3D

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Q: Express the length l of a chord of a circle of radius 8 as a function of its distance x from the…

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Q: Find the equation of the tangent plane to the graph of f(x, y) = In (13x² 10y²) %3D at the point (1,…

A: Solution is written in below steps.

Q: Determine the line tangent to f(x) = 2x2 + 3x + 1 at (-2, 3).

A: The tangent line to a curve at a given point is the line which intersects the curve at the point and…

Q: find the slope of the tangent line to the graph at the given point. (x2 + y2)2 = 4x2y,   (1,1)

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Q: Find all points on the curve y =x3 +-x* + 6x² where the tangent is horizontal. 3

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Q: FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF THE FUNCTION f(x) = 5- x2 AT (3,–4). %3D

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Q: Find the slope of the tangent line to the graph of the function at the given point. F(x) = 2x2 – 5,…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.