Write an expression for the slope of the tangent and normal lines to the curve y = f (x) at the point (a, f (a)) Find equations of the tangent and normal lines to the curve f(x) = (2x^2+1) / (1−3x) at the points with x-coordinates 0 and −1

Write an expression for the slope of the tangent and normal lines to the curve y = f (x) at the point (a, f (a)) Find equations of the tangent and normal lines to the curve f(x) = (2x^2+1) / (1−3x) at the points with x-coordinates 0 and −1

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section1.3: Lines

Problem 3E

See similar textbooks

Related questions

Q: Determine the point on f(x)= 2xe^x where the tangent is parallel to the line y= 2x-12

A: Given, f(x) = 2xex And line : y = 2x-12

Q: Find a rule for the derivative of the product of four functions f,g,h, and k. Use your result from…

Q: Evaluate the second derivative of the given function for the given value of x. 2 3 4 y 3x --,X%= -8…

Q: Derivative of (x-4)2. An over simplified solution would be helpful.

Q: Find an equation for the line that is tangent to the curve y = 2x3 - 8x at the point (2,0). (Type an…

Q: Find the slope and equation of the tangent line to the graph of the equation at a given point. Show…

A: Slope- Point form : y-y1 =mx-x1 ; where ,'m' is slope and x1,y1 point.

Q: equation of the curve at every point of which the tangent line has a slope of -e-².

Q: Consider the equation and the given point. f(x) = (x – 3)(x² + 6), (1, –14) (a) Find an equation of…

A: (a) The equation of the curve and the point is given as,

Q: Describe the First Principle method and the Power Rule method for finding the derivative. Which…

A: In first principle method the slope of the curve is used as a derivative This is called the first…

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

Q: f(x)= (3x²+2x+1)

A: Topic = Derivative

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

Q: Find the slope and equation of the tangent line to the graph of the equation at a given point. 1. y…

A: Given y = 2x² + 4x. Point ( -2 , 0 ) To find slope & equation of tangent line.

Q: find the equation of the curve passing through the point (0,2) and having slope x+ex-sinhx at point…

A: Given problem is : find the equation of the curve passing through the point (0,2) and having slope…

Q: Find equations of all tangent lines to the graph of y = 4x + 40x² + 125x + 118 which pass through…

A: We have given equation of graph y=4x3+40x2+125x+118. We have to find equations of all tangents which…

Q: Find the equation of the tangent line to the curve y=8ln(x3 −63) at the point (4,0)

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

A: f(x) = 2x − x2 We need to find the equation of two tangent lines to the graph of f that passes…

Q: Differentiate the function. Then find an equation of the tangent line at the indicated point on the…

A: Here we differentiate and find the equation of tangent.

Q: f(x)= (4x² +8x+2)

A: We can find the derivative using chain rule as below.

Q: Find an equation of the line tangent to the graph of f(x) = - 2x³ at (– 1,2). The equation of the…

Q: Find an equation of the tangent line to the curve at the given point. y = 2x3 − x2 + 3, (2, 15)

Q: Find the slope of a line tangent to the curve of the implicit function xy + 3y - 28 = 0, at the…

Q: Find equations for the horizontal tangent lines to the curve y = x3 - 3x - 2. Also find equations…

Q: Find the slope the tangent to the curve y² = 3x² + 4 through point (-2, -4)

A: Given: y2=3x2+4 , -2,-4

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

A: y=2x4-3 ; Point (1,-1)Formula:ddxxn=n xn-1

Q: f(x)=√√3x² +6x+2

Q: Consider the given function and point. f(x) = -7x* + 9x² - 2, (1, 0) (a) Find an equation of the…

A: given function is f(x) = -7x4 + 9x2 - 2 we need to find equation of tangent at (1,0) For a given…

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

A: Given function is fx=4x-x2

Q: Find an equation of the tangent line to the graph of the equation: x+y-ex-y=5 at the point (3,3)

Q: The slope of the tangent line equation to the graph of the function y = 5/x-9 at (81,36) i

A: Given:y=5x-9 at 81,36Equation of tangent line:y-y1=mx-x1

Q: Find the equation of the tangent line to the curve y = (x- 1)°(x+ 3)² at the point (2,25). The…

A: Firstly ,find the derivativw of y and then put the value of x coordinate of point to find the slope…

Q: Write the equation of the tangent line to the graph of the function y = 3cosxsinx Leave equation in…

A: y = 3cosxsinx The derivative of any function represents the slope of the tangent line of that…

Q: Passing through the origin (0, 0), there are two lines tangent to the curve y =x + 1, one with…

A: Let (x, y) be the point of tangency on the given parabola. Hence, the tangent passes through the…

Q: Direction: Find the equation of the tangent line to the function at x=a. 5. y = 2x³ + 4x²+7x-9 at…

Q: Find the slope and the equation of the tangent line to the graph of the function f at the specified…

A: The slope of tangent the curve of a function is given by the derivative of the function at that…

Q: Derivative - 16sin4x

A: Given: 16sin4x

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

A: Consider the function y=2x4−3 Point 1,−1

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

Q: differentiation- Can you have an y variable in your answer,

Q: QI. Find the derivative of f(x)= 2x² - - by using the definition of derivative.

A: We have to find derivative

Q: Solve for the equation of the tangent line to the curve y=3x2-4 that is parallel to the line 3x+y=4…

A: The slope of two parallel lines is equal. The product of slopes of lines normal to each other is -1.…

Q: -9) √(x+2)]2

A: The function given is , fx=x2-9x+22. To find the derivative of the function, Apply the product rule,…

Q: Two positive numbers have a product of 81. Find the minimum possible value of their sum.(You must…

Q: Differentiate the function. Then find an equation of the tangent line at the indicated point on the…

Q: Find an equation of the line tangent to the graph of f(x) = 4 - 6x2 at (4, - 92). The equation of…

A: Here need to find tangent to the graph

Q: derivative of f (x)= (9x4 5 - 7x

A: Given:

Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 10 − x2;…

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

Question

Write an expression for the slope of the tangent and normal lines to the curve y = f (x) at the point (a, f (a))

Find equations of the tangent and normal lines to the curve

f(x) = (2x^2+1) / (1−3x)

at the points with x-coordinates 0 and −1

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 8

Trending now

This is a popular solution!

Step by step

Solved in 8 steps with 38 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A function f has the tangent line y=2x+1 at the point (3,7). Find the equation of tangent line of f^-1 at the point (7,3) in slope-intercept form.
Using the mathematical expression of the definition of the derivative, as you learned find the equation of the tangent line to y = 7x - x2 at the point (1,6).
derivative of √x²-4 - 2arcsex x/2, 2<x<4
Solve for the equation of the tangent line to the curve y=3x2-4 that is parallel to the line 3x+y=4 using the slope of tangentline’s (mT) definition. Then, solve for the equation of the normal line too.
Equation of the line tangent to the graph of f(x)=(x)(1-2x)^3 at (-1,1).
Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. y = 4/(x2 − 2x)3, (1, −4)
Find the slope and equation of tangent line y=4-x^3, (-1,5)
Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. Function Point y = (4x + 2)2, (0, 4) y'(0) =
Find equations for the horizontal tangent lines to the curve y = x3 - 3x - 2. Also find equations for the lines that are perpendicular to these tangent lines at the points of tangency.
Explain your understanding of the connection between the derivative of a constant and the slope of the tangent of a function. Use a diagram in your solution
How to find the slope and equation of the tangent line to the graph of the function f at the specified point. f(x) = (x3 + 1)(x2 − 2) point (2, 18)
second derivative of y=x(x-4)3