9) The notion of the derivative of a function x f(x) provides an answer to the following question: a) What is the content of the area under the graph? b) How can a function be represented graphically?

Q: 10. Find the equation of tangent line to the graph of f(x) = 2x – x³, at the point(-1, –1). %3D

A: Find your answer below

Q: Show that no tangent line to the graph of f(x) = tan x has zero slope. What is the least slope of a…

A: Slope of tangent line to f(x)=tanx is given by f'(x)=sec2(x). sec(x)≠0 , so f'(x)≠0  This proves…

Q: Consider the graph of the function f(x) = ln(1 + x²) for x > 0. 1. Find f'(x). 2. At which value of…

A: Ta which value of x the slope of tangent line the greatest.

Q: 7. Use implicit differentiation to find the slope of the tangent line to the graph of x +y = 19 –…

A: Here we will find the slope of tangent line to the given graph,

Q: Find an equation of the tangent line to the graph of f(x)

A: Given function ,         fx=3-Yxx+5at -1,1To find the slope , we differenntiate the function fx…

Q: If tangent line to y=f(x) at the point (4,3) also passes through the point (0,2), what is the value…

A: Given: If tangent line to y=f(x) at the point (4,3) also passes through the point (0,2) To find: The…

Q: 2. Determine the equation of the line perpendicular to the tangent line to the function f(x) = e' at…

A: We will find the equation of the line.

Q: Find the equation of the tangent line to the graph of y = f(x) at r = 3. %3D f(x) = In(x – 6|) y =

A:

Q: Find an equation of tangent line to the graph of f(x) = 2 sin x + cos 2x at (π, 1).

A:

Q: 8. Find the point of the graph of f (x) = xe-2x where the tangent line is horizontal. %3D

A:

Q: Show that the tangent lines to the graph of y = (ex - e-x) / (ex + e-x) atx = 1 and x = -1 are…

A: Here we have to show that the tangent lines to the graph of y=ex-e-xex+e-x at  x=1 and x=-1 are…

Q: 2. Find the points on the graph of f(x) =- where the tangent line is horizontal. x2+2

A: Given f(x)=xx2+2we want to find the point on curve where tangent is horizontal

Q: Find an equation of the tangent line to the graph of fat the given point. f(x) X -

A:

Q: 3. Find the tangent line equation for the given function at the given point: = 3.xy at (3/2,3/2).

A:

Q: Where is the function defined by f(x) = In (x) increasing? Where is f(x) decreasing? Where is the…

A: Given a function: f(x)= ln(x) and the function is defined in the domain x∈(0, ∞)Then, f'(x)=1x

Q: The slope of the tangent line to the graph of the function y= Ttx- cotx at x=0 is O T+1 O T-1

A: Solution is given below:

Q: True or False The slope of the tangent line to the graph of f at (c, f(c) ) is the derivative of f…

A: The slope of the tangent line to the graph of f at c, fc is the derivative of f at c.

Q: 1. FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF THE FUNCTION f(x) = x2 + x - 1 AT (-2, 1). %3D

A: As per our guidelines, we are providing the solution of question number 1 only. Please repost the…

Q: 12, for f(x) n(x) Estimate the slope of the tangent line at the point x (Use decimal notation. Give…

A: Given,

Q: Find the slope of the tangent line at x = 6. for function f(x) = x?tan(2x) %3D

A:

Q: 15 Find the equation of the tangent line to the graph of f(x) at the point where x = 2 Vx3 – x + 3

A:

Q: Is it true that every function y = ƒ(x) that is differentiable on [a, b] is itself the derivative of…

A: Any function y = ƒ(x) is said to be differentiable on closed interval [a, b], it should be…

Q: Prove, using the definition of derivative, that if f(x) = cos x then f ' (x) = - sin x

A: we have to prove by using the definition of derivative that if f(x)=cosx then f'(x)=-sinx   as we…

Q: 1) Find the slope of the tangent line to the graph of f (x) = x3 + x at x = 3.

A: Application of derivative problem

Q: Find the slope of the tangent line to the graph of f(x) = x2 + x at (2, 6).

A: Given :fx = x2+x

Q: show that the function is derivable and that the derivative is continuous.

A: The objective is to show that the given function is derivable and the derivative is continuous.…

Q: 4) Determine the equation of the tangent line to the function 2 f(x) = x at the point (3, 9).

A:

Q: Find slope of the tangent line to the graph f(x)=; at x = 0. 1+cosx

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the…

Q: Find an equation of the tangent line to the graph of f(x) = e×/2 In(x) at its inflection point.…

A: The point of inflection is the point where the second order derivative of the function becomes zero.…

Q: What are the values of x where tangent line of graph of f(x)=1/x is parallel to the line y=−5x+4.…

A: Follow the procedure given below.

Q: 3. Find the equation of tangent line of the function f (x) = e" /x at the point æ 1. Write in the…

A: Given,  The function   fx = exx   We have to find the equation of the tangent line at the point x =…

Q: Find the slope of the tangent line to the function f(x) = tan(cos(ax)) at x =π/2a. Leave your answer…

A: According to chain rule of differentiation ddxfgx=f'gx·g'(x) . Now using this rule differentiate the…

Q: Find the slope of the function F(x) = √√x+1 at the oint (8,3) And find the equation of the tangent…

A:

Q: The tangent line to y=f(x) at (1,-3) passes through the point (3,9). Compute the following: f(1)=?…

A:

Q: Find the equation of the tangent line to the graph of f(x) = 6x ln(x + 4) at x = 4. y =

A:

Q: 5) Use the Fundamental Theorem of Calculus to define of the function fol=sin (x?+!) ant-derivative…

A: According to the fundamental theorem of calculus, the following expression is to be true if F is the…

Q: What is the equation of the tangent line approximation to the graph of a function f at the point (c,…

A: Equation of the tangent line approximation to the graph of a function f at the point (c, f(c)).

Q: Determine the location of any horizontal tangent lines to the graph of f ( x ) = 2 sin ⁡ x − x on […

A:

Q: The derivative and antiderivative of a function are unique. O True False

A: derivative of a function is always unique  but integration is not unique, it depends on constant…

Q: 2. Determine the points on the curve f(x) = sinx-cosx, 0≤x≤27 where the tangent line is horizontal.

A: Find out the points where the tangent line is horizontal.

Q: 7)Determine the points at which the graph of the function has a horizontal tangent line. flx) x2 х-1

A:

Q: Determine the location of any horizontal tangent lines to the graph of f ( x ) = cos ⁡ x − x on [ 0…

A: Given f(x)= cosx To find location of horizontal tangent line we take derivative f'(x)=-sinx At…

Q: 1. Find the equation of the tangent line to the graph of f (x) = x²e-* at x = 1. %3D

A: The given function is: fx=x2e-x In order to find the slope of the given function, find the…

Q: 1. Use implicit differentiation to find the slope and equation of the tangent line given f(x) = x³…

A: Given function is  f(x) = x^3+y^3-9  According to Bartley guidelines we can attempt only one…

Q: ind the slope of the tangent line to the graph of f(x)=(1/x+2) at x=4

A:

Q: 3. Find an equation of tangent line to the given function at the given point: f(x) = 1+ arctan(x/4),…

A:

Q: 7) Find the equation of the tangent line to the graph of f(x) = –sin(x) +3 at x = 4

A:

Q: Find all points on the graph of the function f(x) =2 Sin x + Sin2 xat which the tangent line…

A:

Q: find the tangent line of the function below f(x)=x+4/x and (2,4)

A: This question is based on finding slope to find out tangent line at a point.