2. Determine the equation of the line tangent to the graph of y = x³ + 2x at the point (1,3).

Q: Find an equation of the tangent line to the curve y = 2x +3 that is parallel to the line 8x y+3 = 0.

A: Find an equation of tangent line to the curve y=2x2+3 that is parallel to the line 8x-y+3=0

Q: Find an equation of the line tangent to the curve defined by z2 + 6ry +y = 32 at the point (2, 2).

A:

Q: 4. Find the equation of the tangent line to the curve y=x-2x+3 at the point (2,3).

A:

Q: Find the equation of the tangent line to the curve y = 2 + 4x – x^3 at the point P(-1, -1).

A: To find the equation of the tangent line to the curve, y=2+4x-x3, at the point -1, -1.

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 the tangent to the curve y= (5 – 6x)* at the point (1,1).

A:

Q: Find the equation of the line normal to the tangent at the point (1,2) x’y+xy² = 6. on the curve

A:

Q: Find the equation of the tangent line to the curve y2=6x-3 perpendicular to the line x+3y=7

A:

Q: Find the equation of the tangent line to the graph of y = 2x +- at the point (1,5).

A: We have given

Q: Find the equation of the tangent line to the curve y²(y² – 4) = x² (x² – 5) at the point (0, –2). |

A: Equation of tangent line is given by:y-y1=dydxx=x1·(x-x1)      .............[1]So first find dydx at…

Q: The equation of the tangent line to the curve x2 + y = 9, at (6,-16) is %3| 16 y = (x + 6) – 16 6 6…

A:

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 curve y= (1+2x)^10  , (0,1)

A: First find the derivative of the curve at given point than write the slope intercept form of…

Q: Find an equation of the tangent line to the curve atthe given point. y= In (x3 - 7) , (2 ,0)

A:

Q: Find an equation of the line tangent to the curve defined by x + 3xy+ y = 5 at the point (1, 1).

A: Given  Curve ia x3 + 3xy + y2 =5 at the point(1,1) Find equation of tangent.

Q: Find the equation of the tangent line to the curve y=5x²-1 at x= -1. Y=15x + 9 Y=15x-6 O y= x-6 O…

A: Topic:- application of derivatives

Q: Find the equation of the tangent line to the graph xy^2 − 2y = x^2 at the point (2, −1).

A:

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 an equation of the tangent line to the curve x2+y+y2=13 at the point (-1,3)

A:

Q: ) Find the equation of the line normal to the curve x'y+ y'x = 10 at point (1,2).

A: Slope of a normal to the function y=f(x) at point m,n is given by the value of -dxdy at m,n Equation…

Q: Find the equation of the tangent line to the curve y=1-x² that is parallel to the line 2x-4y=8

A:

Q: Find the equation of the line tangent to the curve of x²y2 – xy + x = 1 at (1, 1).

A: Given: x2y2-xy+x=1 As we know that; The slope of the tangent line to the curve at a given point is…

Q: Find an equation of the tangent line at the point indicated. x3y + y3x = 10; (1,2)

A: Given query is to find the equation of the tangent line at (1,2).

Q: Find the equation of the tangent line to the curve at the given point. y = /2x +1, (4, 3)

A: To find the slope, we find dy/dx at (4, 3) At (4, 3):

Q: At what point on the curve y = 2x²– 3x – 1 is its tangent parallel to the line y = 5x + 2?

A: Given curve is : y=2x2-3x-1 And the given line is : y=5x+2 We need to find the point on the curve at…

Q: Find the equation of the tangent line to the graph ofx^2 * y^2 + 3xy =18 at the point (-2, 3)

A: The given curve is: x2+y2+3xy=18 Differentiating both sides of the equation with respect to 'x', we…

Q: Find the equation of the tangent of the curve y=x^3+(3x)^(-1) at point (1,4)

A:

Q: 12. What is the equation of the tangent line to the curve y = x² – 2x + 1 at point (3,4)? a. у%3D 2х…

A: Since the student has mentioned to solve question numbers (12) and (13), but we can solve only one…

Q: The equation of the tangent line to the curve x² + y² = 64, at (9,-14) is

A:

Q: 25. Find the equation of the line tangent to the curve x2 + y2 = 1 through the point (,).

A:

Q: 2. Write the equation of the tangent line to the curve y = x3 – 6x at the point (2, –4).

A:

Q: Determine the equation of the tangent to the curve y = x - e^-x that is parallel to the line 6x - 2y…

A:

Q: (3) Find an equation of the tangent line to the curve y = 2x² + 3 that is parallel to the line %3D…

A:

Q: 3. Find the equation of the tangent line to (x*+ y°)* +50xy = 0 at the point (2,-4).

A:

Q: find an equation for the tangent line to the graph of y=(5-2x)^2 at (3,1).

A: Explanation of the answer is as follows

Q: Find an equation of the tangent line to the curve x^(2/3)+y^(2/3)=13 at the point (−27,−8).

A: Given:

Q: Find the equation of the line tangent to the curve y =8/x2+4 at the point (2, 1).

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 equation of the tangent line to the curve y= 3x^2 - 2 passing through the point P(-1,1) .

A:

Q: Find an equation of the tangent line to the curve y=x(x1/2) that is parallel to the line y=6+3x

A: y=6+3xBy comparing with y=mx+b, m=3Slope of a line parallel to to y=6+3x is  3

Q: 5. Find the equation of the tangent line to the curve y = x2 - 3x at the place where the parabola…

A:

Q: Find the equation of the tangent line to the curve y=x4 -14x2+17x+40 and perpendicular to the line x…

A: The equation of given curve is   y=x4-14x2+17x+40  On differentiating with respect to x, we get…

Q: . Find an equation of the tangent line to the curve y = x* + 1 that is parallel to the line 32x – y…

A:

Q: Find an equation of the line tangent to the curve defined by x^3+2xy+y^3=4 at the point (1,1).

A: To find the equation of the tangent line at the point (1, 1) to the curve given below.

Q: Determine the equation of the line tangent to y = /1+x³ at the point (2, 3).

A: The given function is y=1+x3. Its derivative is obtained as, dydx=ddx1+x3=121+x3ddx1+x3=3x221+x3 at…

Q: Find an equation of the line tangent to the curve defined by x^3+6xy+y^5=21 at the point (2,1)

A:

Q: Find the equation of the tangent line to the curve y = + 6x at its point of intersection with the…

A: The tangent of any given function is the line that touches the curve of the function at only one…

Q: Find the equation of the line tangent to the curve xy3+xy=20 at the point (10,1). When the equation…

A: It is given that, the equation of the curve is xy3 + xy  = 20. Use implicit differentiation to…

Q: Find the equation of the line tangent to the curve 2(z² + y°)* = 25(z² – y²) at the point (3, 1).…

A: Suppose a line passing through with slope  m then equation of line is .

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: