Use the graph of f(x) = lxl to obtain the graph of g(x) = lxl + 3.

Q: Sketch the graph of the function f(x) = ln 2x  and state its domain.

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Q: How is the graph off (x) = x 3 - l2x 2 + 36x - 16 related to the derivative f'(x) = 3x 2 - 24x + 36?

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Q: Analyze the graph of f (x) = ln(x2 + 2x + 3).

A: The given function is f(x)=lnx2+2x+3

Q: Use the chain rule to find the derivative of f(x)= 5e^-9x^3-6^x^7

A: Given query is to find the derivative of the expression

Q: A T-shirt manufacturer is planning to expand its workforce. It estimates that the number of T-shirts…

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Q: The area of the largest rectangle that can be drawn with one side along the x-axis and two vertices…

A: The diagram below shows the rectangle as mentioned in the problem, The rectangle is symmetric about…

Q: Find the absolute maximum value of the function f(x) = (x - *).

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Q: use the Chain Rule to find the derivative. y = (x4 − x3 − 1)2/3

A: y = (x4 − x3 − 1)2/3 derivative formula ddxxn=nxn-1

Q: Find the derivative of f (x) = x2 + 2x + 2.

A: The given function is, fx=x2+2x+2 To find the derivative of the function, we use the power rule of…

Q: The function y = 2x2 - ln 4x (x 7 0) has one minimum point. Find its first coordinate.

A: Given  y = 2x2 - ln 4x

Q: Sketch the graph of the function and state its domain.

A: Given a function f(x)=ln 2x To find the domain : The domain is given by all the values of x where…

Q: Find the critical point for the function f(x)=-x² +3x+1

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Q: Sketch the graph of the curve f(x)=3x³ - 3x + 2

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Q: Use the Leading Coefficient Test to determine the end behavior of the graph of f(x) = x* – 4x?.

A: To Determine: use the leading coefficient test to determine the end behaviour of the graph of f(x).…

Q: Using the criterion of the first and second derivatives, find the graph of the function a) F(x) = x³…

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Q: Use the Chain Rule to find the derivative. y = (x4 - x3 - 1)2/3

A: To find the derivative y = x4 - x3 - 123.

Q: Use derivatives to sketch the graph of f(x) = (x² – 8x + 16)e².

A: Given

Q: The graph of f(x) = is (increasing/decreasing) over its domain. 3 ()

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Q: Does y = e9-x* – 2 exist? What is the domain & range of the function if it does exist?

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Q: 28)Use the graph to solve a) f(x)0 -fx)

A: To solve the given equation and the inequality , straight from the graph of y=f(x).

Q: Find the x-coordinates of all local maxima using the second derivative test. g(x) = 2° – 3x7 +2

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Q: use the Chain Rule to find the derivative. y = e2x2

A: To find the derivative of y=e2x2 using chain rule. Solution: Chain rule of differentiation states…

Q: Find the derivative of the funchion f(x)=9x-5

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Q: Find the derivative. g(x) = (4x – 2)° – Vr + 8

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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: Find the point on the graph of f(x) = √x that is closest to the point (6, 0).

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Q: Find the local minimum and local maximum values of the function g(x) = 6x2− 4x3 using both the First…

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Q: Use the Chain Rule to find the derivative. y = (x4 − x3 − 1)2/3

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Q: Find the point on the graph of the line f(x)=3x+4 that is closest to the point (6,3) x= y=

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Q: 2) Sketch the graph of the floor function f(x) = x+31 over the interval [-4,2].

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Q: Find a function whose graph passes through the point (1,2/e) and satisfies x^2y'=y.

A: Given differential equation     x2y'=y   and initial condition  at x=1,y=2/e

Q: The line tangent to y = ƒ1x2 at x = 3 is y = 4x - 10 and the line tangent to y = g1x2 at x = 5 is y…

A: The line tangent to y=fx at x=3 is y=4x-10 & the line tangent to y=gx at x=5 is y=6x-27. Put x=3…

Q: Find the derivative of g(x) = 4x 1+4* •

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Q: Find a formula for the linear function with slope −3 and x-intercept 2.

A: Refer to the question.For the linear function with slope −3 and x-intercept 2, use the slope…

Q: Find the vertical asymptote.

A: Given:

Q: The graph on the left was created by transforming f(x) = x'. Determine the equation of the graph.…

A: We need to determine equation of graph.

Q: Find the equation of the horizontal asymptote for the function f(x)= 2 - (x / x2 -25)

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Q: Find the first and second derivatives of the function. f(x) =x4 -3x3 +16x

A: To find the first and second derivatives of the function. fx=x4-3x3+16x

Q: 4. Using at 7 points, graph the function f(x)=2x 10-

A: First we find out the values of y at the different point of x and then make the graph.

Q: Sketch the graph of the function f(x) = ln x − 4 and state its domain.

A: Consider the function: fx=lnx-4 To sketch the graph of the function:

Q: Find the derivative of the function.

A: The given function is gx=3x2-22x+3-2.

Q: Find the first and second derivatives of the function. g(x) = -4x3 + 11x2 + 6x - 51 g'(x) g"(x)

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Q: The derivative of f(x) = x4 + 4e2x is-

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Q: Find the higher-order derivative    1. f ''(x)=16x^(3)-38x^(2)

A: Derivative

Q: The yield in bushels from a grove of orange trees is given by Y = x(1000 − x), where x is the…

A: Rewrite the given function as Y=1000x-x2. Compare the above function with the quadratic function…

Q: Q3\ Find the second derivative of the funetion F(x)= 3x + 2x - 6x2 -4

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.