3. Find the equation of the curve for which y"= 4x³ - 2x and which passes through the point (1, 2) with a slope equal to twice the abscissa.

Q: Find the equation for the curve in the xy-plane that passes through the point (1, -1) if its slope…

A:

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

A:

Q: 5. Find an equation of the line tangent to the curve y = 3x² 1 and parallel to the line 2x – y + 3 =…

A: Explained below

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

A:

Q: At what point on the curve x = 3t2 + 5, y = t3 - 5 does the tangent line have slope ? (х, у) %3

A:

Q: Find equations for two lines that are both tangent to the curve y = x³ – 3x² + 3x – 3 and parallel…

A:

Q: Find an equation of the curve that passes through the point (0, 2) and whose slope is xy?

A:

Q: 15. Find the equation of the curve whose slope at any point is equal to -(y +1)/(x + 1) and which…

A:

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 curve that passes through the point (3, 1), and has the given slope y′ = −…

A: Given that y'=-y5xdydx=-y5x

Q: 3. Find the slope of the graph tangent to the curve y =x* - 2x3 +x that passes through the point (2,…

A:

Q: Find the equation of the lines tangent to the curve x2 + y2 = 4 and parallel to the y-axis ?

A:

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

A:

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

A:

Q: Find an equation for the line that is tangent to the curve y = 3x-3x at the point (1,0).

A: y = 3x3 - 3x P= ( x1 , y1 ) = ( 1,0 )

Q: Find the equation of the family of curves whose slope at any point (x,y) is 3x2+4

A: To find: the equation of the family of curves whose slope at any point (x,y) is 3x2+4  We know that…

Q: 2. Find the slope of the curve at the point indicated. a. y = 5x – 3x²,x = 1 x-1 b. y =,x = 0 x+1

A: Find the slope

Q: Find the equation of the curve that passes through the point (3, 2) if its slope is given by y = dy…

A:

Q: B. Find the slope of the curve at the given point. 1. y = 4 – 3x2 at (-1, 1) 2. y = x2 – 5 at (1,…

A:

Q: 2) Find the equation of the curve whose slope at any point p(x,y) is m =x (x +5)² and passing…

A:

Q: Find the slope of the curve y=x4 at x=3.

A: Find the slope of the curve y=x4  at    x=3.

Q: 4. Find the equation of the curve for which y""= 2x³. The slope of the inflectional tangent at (-1,…

A:

Q: 1. Find the DE of all straight lines with slope and y-intercept equal.

A:

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: 2. What is the slope of the line tangent to the curve 8x3 –- y² = 4 at the point (1,-2)?

A:

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

A: We have to find y

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 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: What is the equation of the line tangent to the curvev= x² – 1 at the point -2,3) y = x+ O y=-4x +…

A:

Q: Find an equation of the curve that passes through the point (1, 1), and has the given slope y′ = −…

A: y'=-9x16yPasses through (1,1)Formula∫xndx=xn+1n+1+C

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

A:

Q: Find an equation of the curve that passes through the point (0, 6) and whOse slope at (X, y) is X/y.

A: Given that: Slope of the curve at (x, y)=xy

Q: The slope of the curve y=x' +3x² – 6x +5 at (1,3) is -

A:

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

A:

Q: 7. Find an equation of the line tangent to the curve y = 3x² – 1 and perpendicular to the line x

A:

Q: Find the slope of a line tangent to the curve y = 15x- 5x at x = 1

A:

Q: Find an equation of the curve that passes through the point (0, 2) and whose slope at (x, y) is x/y.

A:

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

A:

Q: Find an equation of the curve that passes through the point (0, 4) and whose slope at (x, y) is x/y.

A: Solution:find the equation of curuepasses through the point (0,4)slope of cwue is xydydx=xyy dy=x…

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: 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: Find the equation of a line normal to the curve x^2=16y at (4,2).

A: Solve the given problem.

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

A:

Q: Find the equation of the family of curve whose slope at any point (x,y) is 3x^2+4

A:

Q: Two is the slope of the curve y = 4x + x2 at what point?

A: Slope of a curve is given by m=dydx  Use this formula to solve above question.

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: Find the equations of the line tangent to the curve y = x³ + x , where the slope is equal to 4.

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.