1 For f(x) -x² + x + 2, find: a) the equation of the line that is tangent to the graph of f at the point where x = 2. b) the point (as an ordered pair) on the graph of f where the tangent line is horizontal.

Q: What is the equation of the tangent for f(x) = 3(3^x) with the coordinate point x = -1

A: Given: f(x)=3(3x). Take the first derivative wrt x, f'(x)=ddx3· 3x==3ddx3x

Q: Let f(x) = (x – 3)(5x + 7). Find an equation for the tangent line to the graph of f at x = 2.…

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Q: 5. Find using first principles the slope of the tangent to f(x) = x² + 6x + 9 at x = -3.

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Q: For the function ​f(x)=-3x^2 make a table of slopes of secant lines and make a conjecture about the…

A: It is known that the slope of a secant line between points (a, f(a)) and (b, f(b)) is given by:

Q: Find all points (x,y) on the graph of f(x) = 2x3 + 1 with tangent lines perpendicular to the line y=…

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Q: f(x)

A: We will find the equation of tangent.

Q: Find all points (x, y) on the graph of f(x) = x - 3x + 8x + 23 with tangent lines parallel to the…

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Q: If  F(x) = 10x/(1 + x2), find F '(3) and use it to find an equation of the tangent line to the curve…

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Q: The slope of the curve f(x)= at x =1 is

A: given function :

Q: Find an equation for the line tangent to f(x)=x3 +3x2 -2x-8, at the point where x=1

A: To find the equation of the tangent line at point x = 1 for the given curve.

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

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Q: A3) Find the equation of the line tangent to the graph of f(x) = 5x+7x ---.

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Q: 4. Find the equation of the tangent to f (x) = 4x² + 12x, at x = -3. Use first principles.

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Q: If  f(x) = 7x2 − x3,  find f '(1) and use it to find an equation of the tangent line to the curve…

A: Given curve , y=fx=7x2-x3∴ Derivative of fx is                        f'x=ddx7x2-x3…

Q: Find all points (x, y) on the graph of f(x) = x° - 4x + 15x + 10 with tangent lines parallel to the…

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

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Q: For the function f (x) = 2x° – 3x2 – 12x, use the First Derivative Test to find the location of any…

A: The given function is- fx=2x3-3x2-12x To find the critical points of a function- dfdx=0…

Q: At the two points where the curve x² – xy + y² = 36 crosses the x-axis, the tangents to the curve…

A: Given equation of the curve is: x^2 - xy + y^2 = 36 ..................... (1) Differentiating above…

Q: -2, find an If g(x) = xf(x), where f(3) = 4 and f'(3) equation of the tangent line to the graph of g…

A: Consider the given function gx=xfx

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

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Q: Find all points (x, y) on the graph of f(x) = x° - 4x + 20x + 11 with tangent lines parallel to the…

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Q: Let f(x) = (x - 12) / (2x + 6) Find an equation for the tangent line to the graph of f at x = 2 y =…

A: We find f'(x) first using quotient rule

Q: At which x location on the graph of f(x) = -x² - 2x + 15 is the slope of the tangent 0?

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Q: the line tangent to f(x)=x' 3.

A: we have to find the equation of line tangent to  f(x)=x3-x2-5      , at the point (2,-1)

Q: 3. For f(x) = x -5x-6, make a table of slopes of secant lines and make a conjecture about the slope…

A: As we know that the slope of the tangent line is given by, dydxx=a=limh→0f(a+h)-f(a)h If a = 6, then…

Q: Find the equation of the line tangent to the graph of f(x) = −2x² + x + 3 at x = 1. Provide your…

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Q: The graph of f(x)=2x^3+6x^2−144x+6 has two horizontal tangents. what are the positive and negative…

A: See the details solution in below

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

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Q: If f(x) = 9x2 - x³, find f'(2) and use it to find an equation of the tangent line to the curve y =…

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Q: Find the slope and equation of the line tangent to f (x) = x2 +9 at the point (1, 10).

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Q: Let f(x) = 2x + 3 – 17e". Find the equation of the tangent line to the graph of f(x) at the point…

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Q: For the function f(x) = 8x^3-2x^2+2x, Find the equation of the tangent line at x = 2.

A: Please see the answer in Step 2

Q: Determine the points where the curve f(x) = 2x3 + 3x2 – 36x + 1 has a horizontal tangent. -

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Q: If  F(x) = 12x/(3 + x2),  find F '(3) and use it to find an equation of the tangent line to the…

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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: What is the maximum slope of a tangent to the function f(x) = −x3 + 4x − 2?

A: Maximum slopes of tangent to function is 4.

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: Find an equation for the line tangent to the graph of f at (1, 14), where f is given by f(x) = 30 -…

A: Please refer the attached image for complete solution.

Q: Find an equation for the line tangent to the graph of f at (2, 28), where f is given by f(x) = 5x³ –…

A: Given function is fx=5x3-5x2+8. To find an equation of tangent line to the graph at point 2,28.…

Q: If f(x) = 8x2 - x3, find f'(2) and use it to find an equation of the tangent line to the curve y =…

A: The given function is f(x)=8x2-x3

Q: If (x) = 8x² - x, find f(1) and use it to find an equation of the tangent line to the curve y = 8x-…

A: First of all find derivative and slope

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

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Q: Find the tangent line to the equation: f(x) 3x2 + 2x-1, when x= 2 %3D

A: Using equation of tangent formula.

Q: Determine an equation for the tangent to the curve f(x) = 2x3 + 6x2 - 2  at x = -3

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

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

A: Given query is to find the points where tangent is horizontal.

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

A: The tangent line to a curve at a given point is the line which intersects the curve at the point and…

Q: Find the equation of the line tangent to the graph of f(x)= x2 over (3x-4)3 at the point…

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Q: For f (x) = x 3, show that the slope of the secant line over [ -3, x] is x 2 - 3x + 9, and use this…

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Q: Find the equation of the line tangent to the curve f(x) = 4x² - 6x +39 at x = 1.

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