The line tangent to the graph of f at x=3 is y=4x-2 and the line tangent to the graph of g at x=3 is y=-5x+1 . Find the values of (f+g)(3) and (f+g)'(3) .

Q: Find the line tangent to the graph of f(x) = x² + x +1 at xo = 2

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Q: The slope of tangent lines to a curve y=f(x) is given by f'(x)=1/√√x +4x^3-1. If the point (1,6) is…

A: Equation of curve

Q: f(x)

A: We will find the equation of tangent.

Q: For which value(s) of x does f(x)=−x^3/3−2x^2+3x−8 have a tangent line of slope 7?

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Q: 9) Find the equation of the tangent line to the function f(x)=-3x² - 2x at the point where x=1. Give…

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Q: Find the equation of the line that is tangent to the graph of the function f(x) = ln(8x + 6) at the…

A:

Q: 2. Find the equation of the tangent line to the curve y = x² – 2x - 3 that is parallel to the line x…

A: Given: The tangent line to the curve y=x2-2x-3 is parallel to the line x+y=1. To Find: The equation…

Q: An equation of the line tangent to the graph of f(x)= x(1-2x) at the point (1,-1) is

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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: The equation of the tangent line to the graph of f(x) = Vx+1 At the indicated point (3,2) is:…

A: By using the derivative and slope intercept form required tangent equation is :

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: Find the equation of tangent for the implicit function x3 - xy2 + 3y2 + 4 = 0. at the point (1, 2)

A:

Q: 3. Find the equation of the tangent line to the curve y = x2 - 3x + 4 that perpendicular to the line…

A: we have to find the equation of the tangent line to the curve y=x2-3x+4 that is perpendicular to the…

Q: Find an equation of the tangent to the graph of y = f '(x) at x = −1 when f(x) = x3 + 6x2 + 2x.

A:

Q: 4. Find an equation of the line tangent to g(x) = 3x² - x +1 at x= 1.

A: Given function

Q: 14. Find the equation of the line tangent to the graph of f(x) = 2x3-x + 1 at x = -1. %3D

A:

Q: Find the slope m of the tangent line to the graph of the function at the given point and determine…

A:

Q: 3. Find the equation of the tangent line to the graph of f (x) =7-3x-x at x= 1 %3D

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Q: 10. (a) Find an equation for the line tangent to f(x) = x³ + 4x² at the point x = 1.

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Q: The slope of the tangent line to the curve at (x,y) point is defined by 3log3 (1- ) (k +1). If the…

A:

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: A line is tangent to y = x - 2 at (2,6). What is the coefficient of x when the line is in the form…

A: Given curve y=x3-2    ;   (2,6)

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: Find the tangent line of the function f(x) = - 4Vx at x = 4, and the point at which tangent %3D line…

A:

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

A: topic - slope of tangent line to curve

Q: The slope of the tangent line of the graph of the equation xy2-3x² - 2y=-3 at the point (1, 2) is a)…

A: The given equation is xy2-3x2-2y=-3. The objective is to calculate the slope of the tangent line of…

Q: For f(x)=x^4, the instantaneous rate of change is known to be -4 at x=-1. Find the equation of the…

A: Given that: *The function f(x) is f(x)=x4. *The instantaneous rate of change is the slope of the…

Q: Find the equation of the tangent line to f(x) = (x^2) − 4x + 1 at (x=3).

A: We first find f'(3) So the slope is 2

Q: (4) Find the equation of the line tangent to f(x) = 12√ - 2² at the point (4,8).

A:

Q: Find the equation of the tangent line to y = 2r5 - 3x³ at the point where x = 0.7, with coefficients…

A: Methods to find the equation of the tangent at a point helps to find the required answer to the…

Q: 1) Find the slope of the tangent line to the graph of f(x) = x2 - 3 at the point (2, 1). %3D (8…

A:

Q: 7. Find the equation of a line tangent to the graph of f(x) = cotx at x = π/4. Show all steps to…

A: Given :fx=cotx

Q: The tangent line to the curve y = 1/3x^3−3x^2+9x+12 is parallel to the line 8x−2y=3 at two…

A: given: the tangent line to the curve y=13x3-3x2+9x+12 is parallel to the line 8x-2y=3 at two points…

Q: 7. Find the equation of a line tangent to the graph of f (x) = cotx at x = T/4. Show all steps

A:

Q: Find all x-values where f(x) = (x² + 2x – 3)4 has a horizontal tangent line.

A: We find f ' (x) using the chain rule and the power rule. f(x)=(x2+2x-3)4…

Q: At what values of x on the curve y= 2x³+13x²+5x+9 does its tangent lines pass through the origin? In…

A: Given equation of curve: y=2x3+13x2+5x+9……1

Q: 1. For the function f(x) = 4x² + 7x – 2, - (a). Find the slope of the tangent line at x = 4. (b).…

A: Given f(x)=4x²+7x-2 (a) to find the slope of tangent line at x=4 (b) to find the equation of tangent…

Q: Suppose the line y = 8x − 4 is tangent to the curve y = f(x) when x = 1. If Newton's method is used…

A:

Q: Find the equation of tangent and vertical line to the curve g=x+1/x at point (0,1)

A: First we want to check whether the given point is in the domain of the given function.

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

A:

Q: find an equation of a tangent line to the graph of the function (xy^3 +2x^3-x=16) when y=1

A: Slope of the tangent line is the derivative of the given equation at the given point. So…

Q: 3) Find the slope of the curve defined by f (x) = x 3 sin x at x =r.

A: Solution -  Slope of the curve is given by df(x)dx, We have the function f(x), f(x) = x3sinx, Now…

Q: Find all points (x, y) on the graph of f(x) = x° - 5x + 26x + 19 with tangent lines parallel to the…

A:

Q: The equation of a curve is y= 4x²+4lx+12-k, where kis a constant. In the case where k=1, find the…

A: If a line is parallel to the x-axis then its slope will be 0.   Slope of the curve y=f(x) is m =…

Q: .. The slope of the tangent line at any point (x, y) on a curve is given by (x + 2)3 + 1. If the…

A: Explanation of the answer is as follows

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

A:

Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

A:

Q: A curve y = f(x) defined for values of x > 0 goes through the point (1, 0) and is such that the…

A:

Q: Find all r-values where f(x) = (x2 + 2x - 3)4 has a horizontal tangent line.

A: The function f(x)=x2+2x-34. We have to find all x-values where the function f(x) has a horizontal…

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: