Q2: At what points do the graphs of the functions below have horizontal tangents? 1.f(x) = x² + 4x - 1 2.g(x) = x' - 3x

Q: Find an equation of the tangent line to the graph of the function at the given point. y = 7 Ine* +…

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Q: 2. Determine an equation for the tangent line to f(x) = x(x² + 1)3 at x = -1.

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Q: Find an equation of the tangent line to the graph of the function at the given point

A: To find the slope we find y' at x=0, y=0

Q: y = 7x + e5x ; (0, 1) %3D

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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: Find the equations of the tangent lines to the graph of y = ln  x  at x = 1 and x = -1.

A: To find equation of tangent lines at x=1 and x=-1f(x)=lnx

Q: 4. Determine an equation for the tangent line to g(x) = 3 csc(x) – 2 at a = T/4.

A: Solution :-

Q: 3. Find the equation of the tangent line to the curve y = x³ at x=1.

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Q: 8 at x Find the equation of the line tangent to the graph of f(x) = 4x° + 2x2 -4x

A: we have to

Q: Find an equation of the tangent line to the graph of  y = g(x) at x = 2 if g(2) = −3 and g'(2) = 4.…

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Q: Q3: Find an equation for the tangent line to the curve y = etan x at the point where x = 0

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Q: Find an equation of the tangent line to the graph of the function at the given point. y = ln(x7/2);…

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Q: Find the equation of the tangent line to the graph of function at the given point y = 1n x^4 ; (1,0)

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Q: The equation of the tangent line to the graph of f(x)=ln|x at x = -2 is v=²(x+2)+n2 (a) TRUE (b)…

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Q: 3b. Find an equation of the tangent line to f(x)=2x+x-1 at the point Where x 1. %3D

A: The solution of the problem is given in the next step.

Q: Find an equation of the tangent line to the graph of the function                    y = sinh(1 −…

A: Given curve:

Q: Q3: Find an equation for the tangent line to the curve y = etan x at the point where x = 0 (5 marks…

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Q: V3 8. arccos (x ++ y) + x² = 3 when x

A: we have to find out

Q: 3x+ Find an equation of tangent line to the curve: f(x) = EGL

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1) Find the tangent slope to the curve f_((x))=1/ (2x-1) at x=1

A: Given : fx = 12x-1

Q: The tangent lines to the graph of f(x) = x2 grow steeper as x increases. At what rate do the slopes…

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

Q: 2. Find the slope of the tangent line to the curve f (x) = -1 2 at x

A: Given: f(x)=2x

Q: 4. Find all points on the curve y = log (x³ – x) at which the tangent line is horizontal.

A: We will find all the points on the curve at which the tangent line is horizontal using calculus as…

Q: 6) Find an equation of the tangent line to the graph of f (x) = 4 ln z at the point (1, 0).

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Q: b. Find the equation of tangent line to the curve of function f (x) at given point: y = In(x² – 4x +…

A: We have to find the slope of tangent first.

Q: 3. Find the equation of the tangent to the curve 3xy-y²= 7 at the point (.1).

A: Follow the procedure given below.

Q: on the chain rule find the tangent line to graph y=(x+2/x+1)^2, at x=0

A: We have to find tangent line to y , first we will find  value of y at x=0.

Q: 8) Find the equation of the tangent line to the graph of g(x) x3 7 at x = 2. -

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Q: Find an equation of the tangent line to the graph of the function at the given point. y = sinh(25 –…

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Q: 3. For the function g(x) = x' - 2x -1, at what tangent point is the instantaneous rate of change…

A: Instantaneous rate of change of f(x) at x=a is given by f'(a), where f'(x) is the first order…

Q: 5-Find the equation of the tangent to the function y = sin x at x = n/4

A: Given :y = sinx

Q: d the equation of the tangent line to the graph at the specified value of x. y=x√3-x², z = 1.

A: Given query is to find the equation of the tangent.

Q: Find the slope of the tangent to the curve y2 ln(x) + x2y = 7 at (1, 7)

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Q: 12. The slope of the curve y = x2 - e-* at its point of int A. -In 2 В. C. 2+In 4 D.

A: Given query is to find the the slope at inflection point.

Q: 6. Find an equation of the tangent line to y = f(x) : = tan¬(2x) at x = 7

A: Given,

Q: 9. Find the equation of the curve whose y" e*. = - cos x + 6x + 4 with horizontal tangent at the…

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Q: Find the equation of the tangent line to the graph of f(x)= x ln(2x+3) at the point (-1,0).

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Q: 8) Find the equation of the line tangent to the graph of f(x) = x – :- at the point where x = 1.

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Q: 3. Find the equation of the tangent line at point P(2,1) to the graph of the curve f(x) = v3x – 5

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Q: 2. Find the equation of the tangent line to the graph of f(x) = 3x?e-1 - 1, at r = 1.

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Q: Q3)B/ Find the slope of the tangent line to the graph of x² cos(y) = 2y- eš* at the point (1? %3D 00…

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Q: Find all points ( x,y) on the graph of f(x) = 3 x² – 4x with tangent lines parallel to the line y=…

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Q: Determine an equation of the tangent line to y = (e3x - 2)4  at the point (0,1) then solve for y.

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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: 6. Find the equation of the tangent line to the curve y = e when it is parallel to 2x- y=7.

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Q: -2x²+2x+1 Find the equation of the tangent line to the graph of F(x) evI dy at x = 0. sech my

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Q: 13. Given the function f(x) = 4 + x? %3D Find the 8x + 2 equation of the tangent line to the curve 1…

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Q: 2 2х + 2х +1 G(x) = Jsech(x) y e dy

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Q: 1. Find the equation of the tangent line to the graph of f(x) = x?e-* at x = 1.

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.