Suppose you have the function f(x) : 4x2 + 2x + 5. A) What is the exact value of the slope of the tangent line to f(x) at the point a = 4? Answer: m = b) Where does that tangent line (to x = :4 ) cross the y axis? (What is the y-intercept?) Answer: When y =

Q: What is the equation of the line tangent to * f(x) = 4x2 + 2x – 1 at x = 0

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Q: The slope of the tangent line to the graph of the function y = 7V-3 at (9, 18) is

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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: Find the equation of the tangent line to the graph of the function f (x) = V 4x4 +12 at the point…

A: Given: The equation of a function is, f(x)=4x4+12. The objective is to find the equation of…

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

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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: Find the tangent line to the curve y = x + 2x3-2x2 -3x + 3 which is perpendicular to the line x- 3y…

A: Given :y=x4+2x3-2x2-3x+3Line : x-3y=2

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Q: find the point (x,y) at which the graph of y=7x2+5x-6 has a horizontal tangent line.  The function…

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Q: Find an equation of the tangent line to f(x) = 3x +5 at the point (1, 8).

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Q: Determine the point on f(x)= 2x^e where the tangent is parallel to the line y= 2x-12

A: The equation of the curve is  f(x) = 2xe The line parallel to the tangent line on the graph of the…

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

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Q: Find an equation of the tangent to the curve f(x) = 2x2 - 2x + 1 that has slope 2.

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Q: Find the equation of the tangent line to f(x)=xe2x-2 + 3 at the point (1,4).

A: Slope of a tangent of a function at a point is equal to the value of the derivative at that point.To…

Q: What is the equation of the tangent line to the function f(x) = a? + 5x at the point (1, 6)?

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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: For which value(s) of x does f(x)=4x33+2x2+7x−21 have a tangent line of slope 6? Select all correct…

A: we have to find value of  x at which f'(x)=6

Q: The slope of the tangent line to the graph of the function y = 8Vx – 3 at (9, 21) is %3D 1.33 -2.33…

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Q: Find the points on the curve y = 2x3 - 3x2 - 12x + 20 where the tangent line is parallel to the…

A: Given: y = 2x3-3x2-12x+20 Tangent line is parallel to x - axis. To find: The points on the given…

Q: Where does  f(x) = x^3-3x^2+2x-7 have tangent lines that are parallel to y=2x-7?

A: We have to find the coordinates of point at which f(x)=x3-3x2+2x-7 have tangent lines that are…

Q: At what point on the parabola y =  3 x2+ 2x is the tangent line parallel to the line y = 10x −2? Use…

A: First prinicipal : dydx=limh→0f(x+h)-f(x)h

Q: write the equation of the tangent and normal line line of the curve. huow soution your 2. (3.0) f…

A: First, check if the given point lies on the curve, f(x) . If the point is on the curve, then compute…

Q: Find the point (x,y), at which the graph of y = 8x+6x-3 has a horizontal tanger The function y= 8x…

A: Our Aim is to find the point (x,y) at which the graph of y=8x2+6x-3-(i)has a horizontal tangent.

Q: What is the equation of the tangent line to the curve y = x^ + 2x? −x+8 +2x2 where x = 1? y = 7x - 3…

A: Let's find equation of tangent line.

Q: Find the equation of the tangent line to f(x) = 8x² – 5x – 40 at (3,17). %3D

A: Solution of the problem as follows

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

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Q: Find the values of x where the tangent line is horizontal. f(x) = x³ + 3x² – 12

A: The tangent line is horizontal when the slope is equal to 0 dy/dx = 0 y = x3+3x2-12 dy/dx = 3x2+6x…

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

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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: Find the equation of the tangent line to f(x) = x^2 −3x+5 at the point x = 3.

A: Given function , fx= x2-3x+5 at the point x=3 ,at x=3 , f3= 32-3x3+5             f3=9-9+5=5Hence ,…

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: Find an equation of the tangent line to the function y 3x2 at the point P(1, 3). = Soluti

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Q: b) Determine the equation of the tangent line to the grap f(x) = 2x² – x + 5 at the point where x =…

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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: 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: Find the equation of the tangent line to the function f(x)=−2x3−4x2−3x+2 at the point where x=−1.…

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Q: The slope of the tangent line to f(x) = 3x² – 1 at x = 2 is 12. true false

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

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 slope and equation of the tangent line to f(r) = 3+3x at a 3 using the definition. %3D

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Q: 4. At what points on the curve y = 2x³ – 3x2 – 2x + 4 are tangents of slope 10?

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Q: Find the equation of the tangent line to f(x) = (36 + 4x²)¯ at x = Use your answer to (a) to…

A: (a) Given,              f(x)=(36+4x2)-12       at  x=0.

Q: What is the equation of the tangent line to the curve f(x)= 4x2 + 2x -1 at the point x=0 ?  a.)…

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Q: Find the equation of the line tangent to f(x)=3/(2x+1)at the point (1, f(1))

A: Given function is  fx=32x+1

Q: Find all the points on the graph of y=f(x) at which the tangent line has the given slope.…

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Q: At what point on the parabola y=3x^2+2x is the tangent line parallel to the line y=10x-2? Use first…

A: We have to find the point.