Given the function below f(x) V36x3 Find the equation of the tangent line to the graph of the function at x = 1. Answer in m + b form L(x) = Use the tangent line to approximate f(1.1). L(1.1) = Compute the actual value of f(1.1). What is the error between the function value and the linear approximation? Answer as a positive value only. |error| 2 (Approximate to at least 5 decimal places.)

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 3 if g(3) = -5 and g'(3) = 2.…

A: Here, y = g(x)  and g(3) = -5 i.e. when x1 = 3, then  y1 = -5 and g(3)=2 i.e. At x =3, the slope, m…

Q: find the equation of the tangent line at x=-6 for f(x)=x^3/2. write the answer in the form y=mx+b

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Q: Q5: Does any tangent to the curve y vx cross the x-axis at x--1 If so, find an equation for the line…

A: It is required to find if any tangent to the curve y=x cross the x-axis at x=-1. First find the…

Q: (a) 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: (3) Find the equation of the line tangent to f(x) = 2x³ - 2x2 +1 at x = 1. [Hint: f'(a) is the slope…

A: We find the slope of f(x) at x=1 by finding f'(1)

Q: Find an equation of the tangent line to the graph of the function at the given point. y = (e4x −…

A: We first have to find y'We apply exponent rule and chain rule.y'= 8(e^(4x))*(e^(4x)) -4)

Q: Find an equation of the tangent line to the graph of the function at the given point.   y = (e3x −…

A: Given,  The equation of the curve y = e3x-42  We have to find the equation of the tangent line at…

Q: 12. Given the point ( 2, 1) on a tangent line to the curve ƒ(x) = x² − 2x + 5 find the point(s)…

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Q: For which value(s) of x does f(x)=2x33−2x2+4x+14 have a tangent line of slope 2? Select all correct…

A: we have to find value of x at which slope of f(x) is 2means f'(x)=2

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

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 2 if g(2) = -6 and g'(2) = 4.…

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Q: Q3 / Answer one of the two following branches: A- Using L'Hopital rule for solving the following…

A: L 'Hospital Rule

Q: 4. What is the slope of the curve of f(x) = v2x + 1 at x = 4? а. 3 b. - с. d. ! e. None of the above

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Q: Solve the problem. Find where the tangent to the curve f(x) = V+1 that has slope . O x = 3 O x = 1 O…

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 3 if g(3) = -2 and g'(3) = 6.…

A: we are given y=g(x),g(3)=-2,g'(3)=6

Q: 5. Find the slope of the tangent at the given points for the function S4 – x², x 15 а) P(- 1, 3) b)…

A: Topic- application of derivatives

Q: Find an equation of the tangent line to the graph of f(x) =2- 5x at (2, – 18). The equation of the…

A: A function is a relation which maps each value in its domain to exactly one value in its range.…

Q: (A) Find the equation of tangent and normal to the curve x? + 2y = 9 at (-1, –2). (B) Use the first…

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Q: The derivative of f(x) = %3D 3. 5' attains its maximum value at r =

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Q: Find an equation of the tangent line to the graph of  y = g(x) at x = 6 if g(6) = −2 and g'(6) = 5.…

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

A: The equation of tangent line passing through the point x1,y1 is y-y1=mx-x1, where m is slope. The…

Q: 3. The slope of the tangent line to f(x) = A tan(x) is 1/2 when x = 27/3. Deter- mine the equation…

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 4 if g(4) = -3 and g'(4) = 5.…

A: y=g(x) and g(4)=-3 , g'(4)=5 we have to find the tangent line of the given function y=f(x)

Q: 1. For the function f(x) = 2x? + 7x – 3, - (a). Find the slope of the tangent line at x = 2. [1Mark]…

A: The answers are : (a)  15  (b) y = 15x - 11   The detailed solution is as follows below:

Q: Find h'(-2) if h =fog, f(x) = 6x² - 1 and the equation of the tangent line of g at -2 is y = -2x +…

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Q: 49. Find an equation of the tangent line to the graph of y = 8/(x² + 4) at (a) (0, 2); (b) (–2, 1).

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

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Q: Given the function g(x) = 8x° 36x + 48x, find the first derivative, g'(x). g'(x) = Notice that g'(x)…

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Q: Given the function g(x) = 4x° – 36x?+ 96x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

A: Given that, the function is g(x) = 4x³ - 36x² + 96x We have to find the g'(x),g"(x) and have to…

Q: Find an equation for the tangent line to the graph of the function F(x) = V3x2 + 9 at the point (3,…

A: To find the equation of tangent of given equation.

Q: Find h'(-3) if h = f o g, f(x) = -8x? + 6 and the equation of the tangent line of g at -3 is y = 7x…

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Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = 11 e*+…

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Q: When observations begin at t=​0, a cell culture has 1100 cells and continues to grow according to…

A: Here a function is given which represents growth of the cells. We have to find the derivative of the…

Q: Find all values of x at which the tangentline to the curve y = 2x+13 has the y-intercept 2. x+6…

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Q: Q4\ Find the slope of the function F(x) = √√x+1 at the point (8,3) And find the equation of the…

A: To find the slope of the function at the given point and also the equation of the tangent line at…

Q: Find h'(-3) if h = f o g, f(x) = 8x? – 2 and the equation of the tangent line of g at -3 is y = -3x…

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Q: Q5: Does any tangent to the curve y = vx cross the x-axis at x=-1 If so, find an equation for the…

A: To find: The equation of tangent to the curve y=x if possible. Given: The equation of the curve y=x.…

Q: Find all values of x at which the tangent line to the curve y = 2x+3 x+1 has the y-intercept 2.…

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Q: 3. A function is defined by the equation y = V3x + 4, where does the slope of the tangent line equal…

A: Given,           A function is defined by the equation y=3x+4 and the slope of the tangent line…

Q: Q3 Find the equation of the tangent line to the function f(r) =x+7 at r 1. Show your work.

A: f(x) =x3 +7 Let y = f(x) = x3 +7, we have to find the tangent at x=1 , so value of y at x=1 is  f(1)…

Q: Find the equation of the line tangent to the graph of f(x) = −3cos(x) at x = −π/3   Give your…

A: First, find the point of tang-ency. We know the x value we now have to find y value  Substitute in…

Q: Find all values of x at which the tangent line to the curve y = 2x+17 has the y-intercept 2. x+8…

A: This question is related to curve and tangent, we will use differentiation to solve it.

Q: 12. Given the point ( 2, 1) on a tangent line to the curve f(x) = x² – 2x + 5 find the point(s)…

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Q: 1. For the function f(x) = 3x? + 8x – 2, (a) Find the slope of f(x) at x = 3 | (b) Find equation of…

A: According to the bartleby guidelines, for more than one questions asked, only the 1st question…

Q: 13x Ca) If F(x) = find F'(3) and use it to find an equation of the tangent line to the curve y = 13x…

A: Given function is : Fx=13x4+x2 To find the value of F'3 and to find the equation of tangent to the…

Q: 1. For the function f(x) = 4x? + 6x – 6, (a) Find the slope of f(x) at x = 4 (b) Find equation of…

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 4 if g(4) = -6 and g'(4) = 5.…

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 4 if g(4) = -6 and g'(4) = 3.…

A: The tangent line is a Straight line which is a tangent to the curve at the point. The point here…

Q: 2. Write the equation of the tangent line to the curve y = x2 -x-2+ 2 at the point P(1, 2). 3. Use…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…