Consider the function: f(x)= 4x^2-9/-x^2+x+6. Find the equation of the vertical asymptote(s)(if any).

Q: Apply derivative to determine the vertex of the parabola y = x² + 2x + 2.

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Q: Find an eqaution of the line tangent to the graph f(x) = 3x2 - 5x at the point (1,-2).

A: fx=3x2-5x Slope of the tangent line is the derivative of the given function at the given point. So…

Q: Graph the function y=-sin2x on [-pi,0]

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Q: Find the equaiton of the tangent line for the function f(x)=x+3/x-3 at the point (4,7).

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

Q: Please show step-by-step solution!

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

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Q: Use second derivative test, If f(x) = 25x + 10 then f(x) has a 3 local maximum at the point_

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Q: Find derivative using product or quotient rule

A: f'(x)=((x2)'(x+3)(4x-1)-x2((x+3)(4x-1))')/((x+3)(4x-1))2       (Using quotient rule)…

Q: How is derivatives utilized in solving for the dimensions and total area of a box?

A: Here we to write how is derivatives utilized in solving for the dimensions and total area of a box.

Q: The slope of the tangent line to the graph of the function y = 2x3 at the point (2, 16) is lim2"…

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Q: What is the y-coordinate of the y-intercept of the secant line of the square root function at x=1…

A: Here we have to find the y-intercept of the secant line

Q: apply 1rt and second derivative to sketch graph  1)f(x)=3+7e^(-0.2x) and  2)f(x)=ln(2x+4)

A: In the question we have to draw the graph.

Q: Sketch the curve if y' is negative and y'' is negative on the interval of (-infinity, -3) with a…

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Q: Use symmetry, first derivative, second derivative, and asymptotes to graph function:y: 2-x

A: The given function is y=x2-12-x ...............(1)

Q: Explain how to write an equation of the tangent line to the graph of f(x) = x2 at (2, 4).

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Q: sketch the graphof the function and state its domain. f (x) = 4 ln(x − 2) + 1

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: how would you, using a limit def. of a derivative at a point find f'(-1) for the function f(x). =…

A: Hint:

Q: Sketch the graph with details of the function below by using the first and second derivative tests.…

A: We will use following properties of f(x) to draw its graph  # vertical asymptotes are vertical…

Q: Find the derivative of f(x)=8x - 5x+2 using first principles (i.e., use the definition of the…

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Q: Use the second derivative test to find the local extrema for the function. y = 3x5- 25x3 + 60x + 20

A: We can use the application  derivative in order solve the given problem.

Q: 4 6. ν- x3

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Q: Find the derivative of the function f(x)=2x2 using the limit definition.

A: Limit definition of derivative of f(x) is  f'(x)=limh->0f(x+h)-f(x)h

Q: Find the slope m of the line tangent to the graph of the function f(x) = 5 - 6x at point (-1, 11)

A: Given:  f(x)=5-6x                y=5-6xDidderentating y=5-6x   with respect to 'x'  and substituting…

Q: Use Intermediate Value Theorem to show that the equation

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Q: a) f'(-3) where f(x) = 5-3x

A: Derivative using definition

Q: Find the equation of a tangent line to the graph of f(x) = x² – 2X at (-2,8). TYPE IN THE EQUATION…

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Q: Find the slope of line drawn tangent to the function. f(x)=x2+7, at the point (-2,11) by using the…

A: Shape of tangent line to the curve is given by first derivative of curve at given periodDerivative…

Q: Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.

A: Consider the given: The numerical derivative does not exist a point in three cases: 1) when there is…

Q: (f°9)(x) if f(x)=2x3 +1 and g(x)=6x +5

A: We have to find the composition of the function then have to find the second order derivative.

Q: rconh(3x+1) - 5t +ldt f(x)= sinh³

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Q: 1. у %3D 4x2 — 3х — 2.

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Q: Differentiate and simplify: f(x) = arcsin ( 2x / x2 + 1 )

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Q: Find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis and a tangent…

A: We have to find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis…

Q: Estimate the derivative of the function f (x) = -3 at the point a = 3. %3D

A: Here given as fx=x3-3 Differentiate with respect to x f'x=ddxx3-3=ddxx3-ddx3=13

Q: Use the second derivative test to find the extreme values of the function f(x) = 13 -3z2-24x

A: Given: f(x)=x3-3x2-24x To find the extreme value of the function.

Q: Find the derivative of the function by definition. 1- V2x+3

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Q: Graph f(x) x'- 3x-9x + 2. 3r2

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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: How do you use the second derivative test to analyze concavity of a function?

A: We know that, If the second derivative of the function f(x) is defined on an interval (a,b) and…

Q: What is the derivative of a function f(x) = 4x³ – 3x2 at a number a? %3D

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Q: Sketch the graph of y= x²+ - by using the properties of the derivative. 2

A: To sketch the graph

Q: Find the directions in which the function increases and decreases most rapidly at Po-

A: Given, fx,y,z=4lnxy+lnyz+lnxz, P01,1,1 Direction in which function f increases is given by, u^=∇f∇f,…

Q: Use Second Derivative Test to find the location of all local extrema for f(x) = 2x3+21x²+ 36x-1

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Q: Joha Find the derivative of the 1 1- f(x)= 2x+3

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Q: Express the length l of a chord of a circle of radius 8 as a function of its distance x from the…

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Q: Apply the first derivative test to indentify all relative extrema. f(x) = ¹²-2x+1

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Q: f(x) = (6x – 7)(2x + 3) %3D

A: Given  f(x)=(6x-7)(2x+3)

Q: Describe how you would use the second derivative to determine a local minimum or maximum.

A: Given data is: How you would use the second derivative to determine a local minimum or maximum

Q: Estimate the slope of the tangent to the function f(x) = (x + 1)^2(x - 4) at the point of abscissa…

A: Introduction: A tangent line is one that intersects a curve at the so-called point of tangency.…