1. Let f(x) = x³ – 5x + 2, Use Derivative Rules to find the following: a) Find the equation of the line tangent to f(x) and the point (-2, 4) b) Find the equation of the line perpendicular to the line in part a; this is called the normal line c) Find the equations for the horizontal tangents of this curve. 2x+1 2. Use Derivative Rules to find the derivative of g(x) = x2-1

Q: 3. Find the equation of the tangent line to the curve f(x): at the given point (-5,5) x+4

A: Given  function

Q: 1. Find the equation of the tangent and the normal line for the equation at the given point below: y…

A: Given, y=x3-6x+2 at the point (2,-2)

Q: 8) Find the slope of the tangent line to the graph at the given point. (x² – y³)² = 4x²y - 3x -…

A: Consider the equation and the point

Q: Find (a) the equation of the secant line through the points where x has the given values, and (b)…

A: Given f(x)=3x2-5x+7, x=2, x=4

Q: Find the slope of the tangent line to the graph of xy^2 + x^2 + y^2 = 9 at the point (0,3)

A:

Q: Find an equation of the tangent line to the curve at the given point y = 4x2 – x, (1, 3)

A:

Q: B. Find the slope and the equation of the tangent line to the curve 1. y = 4 - 3x at (- 1, 1) 2. y…

A: We need to find the slope and the equation of the tangent line tothe following curve:3. y=3x2+2 at…

Q: Find the equation of the tangent line to f(x)=xe2x-2 + 3 at the point (1,4).

A: Slope of a tangent of a function at a point is equal to the value of the derivative at that point.To…

Q: Find y' and the slope of the tangent line to the graph of (3x- 2y)° = 2y2 - 9 at the point (1,2).

A:

Q: 3. Find the equation of the tangent line to the curve f (x)= (1+2x)'" at the point (0,1) in…

A:

Q: Find y′and the slope of the tangent line to the graph of ​(2x-5y) 5=4y2 -3 at the point ​(3​,1​).

A: Find y′and the slope of the tangent line to the graph of ​(2x-5y) 5=4y2 -3 at the point ​(3​,1​).…

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

A:

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

A:

Q: 3. Find the equation of the tangent line to the graph of x y + 7xy = 30 at the point (-5, 2). %3|

A:

Q: 1. Find the slope of the line tangent to the graph of f (x) = x³ In (x² – 5x + 7) at x = 2. - Do NOT…

A: We have to find slope to given equation by derivative.

Q: (B): Find an equation for the tangent and normal Line to the curve (y 2x +4x-3) at (x1)

A:

Q: Find an equation of the tangent line to the curve at the given point. x2 (4, 16) y

A: Given ex2-y=x2y To find equation of tangent at the point 4,16

Q: _1. What is the slope of the tangent line to the curve y = 3x² – 5 at point (-1,-2)? a. -5 b. -6…

A: Using Derivatives & Application of derivatives

Q: 1 Find the two points on the curve y=- at which the tangents have as slope of -.

A: Given,            The curve y=1x at which the tangents have as slope of -12.To find : The two points…

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

A:

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

A:

Q: 2. Find the equation of the tangent line (in slope-intercept form) to the curve y=xvx that is…

A:

Q: (a) Find the slope of the curve at point P and write the equation of tangent line at point P. 2x2…

A:

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: 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: B. Find the slope and the equation of the tangent line to the curve 1. y = 4 - 3x at (- 1, 1) 2. y =…

A:

Q: Suppose f (x) = (x 2 − 2x) (3x + 2).What is the equation of the line normal to f(i.e., the line…

A:

Q: Find the equation of the tangent and normal line using the stipulated conditions   1.) y = x2 - 5x…

A: Given the equation is y = x2 - 5x The point of intersection line y=6 The equation of the tangent is…

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

A:

Q: . Find the gradient of the TANGENT LINE at the given points y = 4 - 3x2         at (-1, 1) y = x2 -…

A:

Q: 1 - Find the equation of the tangent line to the curve y = 3 5 x2 +6x 2 11 at its point of…

A:

Q: 12. (a) Use the definition of derivative to find the slope of the tangent line to the curve f(x) =…

A:

Q: 4. Find the equation of the tangent lines to the curve y = √x and perpendicular to the line 14x +…

A: We have to find the tangent

Q: Determine the values of p, q, and r so that the function f(x) = px° + qx² + rx will have an…

A:

Q: 6. Determine the equation of the line tangent to y = x+ tan r at the point (7, 7).

A: As per the company policy i can answer only first question for you, More than that leads me towards…

Q: find the slope of the tangent line to the curve at the given point. x^2 + 4xy + y^2 = 13, (2,1)

A:

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

A:

Q: Use implicit differentiation to find an equation of the tangent line to the devil's curve,defined by…

A:

Q: Find all points (x, y) on the graph of y with tangent lines perpendicular to the line y = 4x - 5. (x…

A:

Q: 2. Find the slope of the tangent line to the curve y? + yx² + x² – 3y? = 0 at the point (0, 3).

A:

Q: 2. Find the slope of the tangent line to the curves: (a) xy + y³ = 12 at the point (2, 2), (b) 3x4/3…

A: This question can be solved using the concept of tangent and normal using application of…

Q: A) Determine the equation of the tangent line to the curve xsin(y) – x²cos(y) = 1 at the point (1,4)

A:

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

A:

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

A: Given,

Q: Find the equation of the line that is perpendicular to the tangent line to f(x) = x4+1 at x = 2 and…

A: Answer and explanation is given below

Q: Find an equation of the tangent line to the curve at the given point. f(x) = 7x2 - x³, (1, 6) y =

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.