Use calculus and show the test to find the intervals on which f is increasing and decreasing. f(x) = x3-12x

Q: Let the function f be defined by the equation y = f(x), where x andf(x)are real numbers. Find the…

A: Explanation of the answer is as follows

Q: Find the intervals of concavity for the function and state the points of inflection. a.…

A: Given that functions are      (a) f(x) = x4 -2x3 +x -2     (b) f(x) = x2/(x2-4) Here we have to find…

Q: A: Find f-¹(x) and identify the domain and range of f¹(x). As a check, show that f(f(x)) = f(f(x)) =…

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Q: Identify the open intervals on which the function is increasing or decreasing. g(x) = x2 – 4x – 12…

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Q: Find the intervals in which the following functions are increasing or strictly decreasing  x2+2x-5

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Q: Determine the open intervals on which the function f(x) = x3 − 3x2 + 2 is increasing,decreasing, or…

A: Function is increasing if it has positive slope, decreasing for negative slope and constant if slope…

Q: a) Find the intervals at which the function is increasing or decreasing. x2 f(x) = 16 – x2

A: f(x) = x²/(16 - x²) So, f'(x) = [(16 - x²)•2x - x²•(-2x)]/(16 - x²)²  So, f'(x) = 32x/(16 - x²)²…

Q: Given the function f' (x) = -x + 12x² – 36x, determine all intervals on which f' is increasing.

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Q: Determine the open intervals on which the function f(x) = √(x2 − 1) is increasing,decreasing, or…

A: f(x)=x2-1

Q: Find all discontinuities of f(x) = +5x Are they removable or not? %3D 3-25x

A: The function f(x) is, f(x)=x2+5xx3-25x=x(x+5)x(x2-52)=x(x+5)x(x-5)(x+5)=1x-5 The denominator of the…

Q: Determine the open intervals on which the function f(x) = x3 − 3x2 + 2 is increasing,decreasing, or…

A: f(x)=x3-3x2+2

Q: the function f(x) = 2x + 2, find all values x for which f(x) = 19.

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Q: Use interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c)…

A: Given the graph

Q: Determine the values of x for which f(x) is continuous. Write the answer in interval notation. if x…

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Q: Determine the open intervals on which the function f(x) = √(x2 − 1) is increasing,decreasing, or…

A: Given: fx=x2-1 For finding increasing, decreasing interval for given function, we draw graph of it…

Q: Find all values of x such that f (x) > 0 and all x such that f (x) < 0, and sketch the graph…

A: Find all values of x such that f (x) > 0 and all x such that f (x) < 0, and sketch the graph…

Q: Use the definition to find f'(-3) where f(x) = x² + 5, then decide if f is increasing or decreasing…

A: Given function is fx=x2+5. To find f'-3 using the definition and then to decide if function is…

Q: Find real values of x for which f(x) = 0. f(x) = x2 − 81

A: Find real values of x for which f(x) = 0.

Q: . Let f(x) = x4 − 3x2 + 2. Find the intervals where f(x) is increasing, decreasing, concave up and…

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Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

A: f(x) = 2x4 - 144x2 + 4 f'(x) = 8x3 - 288x = 8x(x2 - 36) = 8x(x - 6)(x + 6)

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

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Q: Find the domain of the function. 9. if x=2 f(x) = x2 if 1<x< 2 The domain is (Type your answer in…

A: Domain

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = xe-x²/98…

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Q: Using the function g ( x ) = 2x³ - 6x , determine the intervals where the - function is increasing…

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Q: Determine the open intervals on which the function f(x) = ∣x + 1∣ + ∣x − 1∣ is…

A: f(x) = ∣x + 1∣ + ∣x − 1∣

Q: Find the absolute extreme if they exist, as well as all values of x where they occur, for the…

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Q: Use calculus to sketch the graph of the given function. (a) f(x) = 3x* – 4xr

A: Consider the given function, fx=3x4-4x3 Here we need to sketch the graph of the given function using…

Q: Determine the open intervals on which the function is increasing and on which the function is…

A: The given function is f(x)=x3+3x2-9x  differentiate with respect to x,

Q: Find the absolute maximum and absolute minimum values of f on the given interval F(x) = xex2/98 [-3,…

A: Given function is

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing.…

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Q: Given the function f' (x) = -x3 + 12x2 f' is incileasing. 36x, determine all intervals on which

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Q: let f(x)= -4+3e^x what is the range of f(x) using interval notation? what is the domain of f(x)…

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Q: Use interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c)…

A: Given:

Q: Let f(x)= x2e9x. f'(x)= 9x2e9x + 2xe9x. Find the intervals where f(x) is increasing and…

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Q: Find the intervals on which f is increasing and decreasing. fox) = 3x* - x² + 9

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Q: Define the domain of f(x) x + 16 x² + 10x + 21 Use interval notation for your answer. The domain of…

A: Given function is fx=x+6x2+10x+21 To find: Domain of function in interval notation. Concept: Domain…

Q: 3. Given f (x) = 5x² and g(x) = Vx – 3 , what is the domain of (f • g)(x)? Write your answer in…

A: f(x)=5x2, g(x)=x-3

Q: Given f(x) = x4 − 2x2 . Find the intervals of concavity

A: We find f"(x) using the power rule.

Q: Let f(x) = x − 9 and  g(x) =square root of x+9.  Find the rule for the function. gf

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Q: Find and classify the extreme values of f(x) = 6x4 – 4x over the interval [-2, 2].

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Q: Determine the intervals upon which the given function is increasing or decreasing. f(x) = 3x³ + 9x?…

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Q: Find the differnce quotient with steps  use the function f(x)= x^2-16 and using formula…

A: Given that f(x)=x^2-16 differnce quotient f(x+h)-f(x)/h

Q: Graph the function f (x) = x3 − x 2 – 6x to estimate the local extrema of the function. Use these to…

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Q: Use calculus to sketch the graph of the function given by f(x) = x³ – x² – 6x+4. Show all steps…

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Q: Using the definition of a function being measurable, show that the function f(x) = r-10 is…

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Q: Let f(x) = x4 - 2x2.  Find the intervals on which f is increasing and decreasing, and give the…

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Q: Find the constant a such that the function is continuous on the entire real number line. x 6 %3D

A: F is a piecewise function.  The only point it can be discontinuous is at x=6 because their the…

Q: Use the graph to estimate the open intervals on which the function is increasing or decreasing. Then…

A: Starting from the left, we see that the curve goes downwards from -∞ to -1, so the function is…

Q: Find the intervals where the piecewise defined function is negative, and enter your answer in…

A: Consider the given graph. Observe that, from x=-5 to x=-4 and from x=1 to x=5, the graph of the…