Find all points on the graph of the function f(x) = 2sin(x) + sin²(x) at which the tangent line is horizontal. Hint: what is the slope of a horizontal line?

Q: Find an equation of the tangent line to the graph of f at the given point   f(x)=(2x+1)/(x+2),…

A: Given  fx=2x+1x+2 To find tangent differentiate the function f'x=x+22-2x+1.1x+22     =2x+4-2x-1x+22…

Q: Find an equation of the tangent line to the graph of the function f(x) = tan2(x) at the point

A: topic - equation of tangent line to curve

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 equation of the tangent line to the graph of f (x) = -4e2* at the point (0, -4). Hinti Sh

A: Explanation of the answer is as follows

Q: Find an equation of the tangent line to the curve at the given point. f(x) = 3x² – x³, (1, 2) -…

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Q: Find the point of tangency and equation of the tangent line of the following functions given a…

A: First we find slope of the function y=5x2-x dydx=10x-1dydxx=1=10(1)-1dydxx=1=10-1dydxx=1=9 At x=1,…

Q: Find the slope-intercept equation of the tangent line to the graph of f(x) =√x at (1, 1).

A:

Q: Find the equation of the tangent line when x = a on the function (x) = -5 cos(x)

A: slope-point form : (y-y1)= m(x-x1) ; where 'm' is slope and x1,y1 is the point.

Q: (b) Find the equation of the tangent line to the graph of the equation sin-"(x + y) = ;r² 2 at the…

A: Topic = Derivative

Q: find the equation of the tangent line, in standard form, to the curve y=sin2x-cos2x at the point…

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Q: Find an equation of the tangent line to the graph of the function at the given point. y = xsin(x),…

A: We tale ln on both sides then differentiate both sides with respect to x

Q: f (x) = x² + Vx at the point where x = 1

A: We have to find equation of tangent line for the given function at the specified point: fx=x2+x at…

Q: f (z) = sin (3,/7) at the point 72,0)

A:

Q: Consider the following. Function Point (--) f(x) = tan2 x (a) Find an equation of the tangent line…

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Q: Find an equation of the tangent line to the graph of the function f defined by the given equation at…

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Q: f (x) = x² + Vx at the point x = 1

A: Consider the given: fx=x2+xf1=12+1f1=1+1f1=2Find the derivative:f'x=2x+12xAt…

Q: Find the points on the interval [0, 2π) where the graph of the function  f(x) = 2 sin(x) + sin2(x)…

A: Given:f(x)=2sin(x)+sin2(x),       [0,2π)

Q: V. Determine the equation of the tangent line to the graph of g at the point where r = 1 if g(x)= In…

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Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = el-x,…

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Q: Find an equation of the tangent line to the graph of f at the given point.            f(x) = (1 +…

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Q: (B): Find the tangent equation to the curve y = sin² x at point x F.

A: We can find the tangent equation at the given point as below.

Q: Does the graph of the function y = 6x + 3 sin x have any horizontal tangents in the intervalocce O…

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

A: Solution:Given          f(x)=sec-1(ex);              (ln 2, π/3)To find the equation of the line…

Q: Find the equation of the tangent line to f- at the point P (-3, 1) for f(x) = - 1- 2x Provide your…

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Q: Find all the values of x where the function f(x) = 5e* sin x has a horizontal tangent line.

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

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Q: Find an equation of the tangent line to the graph of the function f(x) =tan(2x) at (?/8,1)

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

A: Given,           fx=1+cosx1-cosx , π2,1

Q: Find an equation of the tangent line to the graph of the function F(x) = tan²(x) at the point 1 -4x…

A: Here we find the tangent equation.

Q: Find the equation of the tangent line to the function f(x) = –3x² form y - 2x at the point where x…

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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: Find the equation(s) of the tangent line to the graph of f(x) = x² +1 passing the point (3, 1).

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Q: Determine the equation of the tangent line to the function g(x) = (2ex)/x at the point, (2, e2).

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

Q: Suppose that the tangent line to the graph of f(r) = *) at r=1 is equal to the tangent line to the…

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

A: Consider the function  f(x)=x2−1x2+x+1 Point (1,0)

Q: Find the equation of the tangent line to the function f(x) = -3x – 2x2 – 1 at the point where x =…

A: Given : fx = -3x3 -2x2 -1

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

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Q: Find an equation of the tangent line to the graph of ​f(x)=ex​, where x=−0.3.   The equation of the…

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Q: For what values of x does f(x) = 3x+6 sin x have a horizontal tangent line?

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Q: Does the line tangent to the graph of f(x) = sin(2x) +5x at x = lie above or below the graph of f?…

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Q: Find an equation of the tangent line to the graph of the function at the given point.   f(x) =…

A: Given,     f(x) = ln(9(x+4)/x); (-9/2,0) Let m be the slope of required tangent line.

Q: Find the equation of the tangent line of the function at the given point. 9. f(x) = 3x+2 (0,-2) x-1…

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Q: Find the slope of the tangent line to the graph of f(x) at the point (1,2). The function is…

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Q: Find all points the graph of f(x) = 2 sin x + sin?x where the tangent line is horizontal on

A: Solved below

Q: Find an equation of the tangent line to the graph of the function at the given point. y = x2ex −…

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

A: First find the slope of the tangent line then write the equation of tangent line in slope intercept…

Q: Find an equation of the tangent line to the graph of the given function at the specified point. x2 -…

A: Our Aim is to find an equation of the tangent line to the graph of the given function…

Q: ) Find the equation of the tangent line to the curve y = 2x cos x at the point (π,-2π). The equation…

A: we have to find tangent to f(c) at x=pi

Q: Find the slope of the tangent line to the graph of f(x) = √√√x-2 at x = 6. Provide your answer…

A:

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: