Consider the following function: f (x) = -1/2 x^4 +16x^2 -4 Determine f′(x) and f′′(x).  Determine where the function is increasing and decreasing. Enter your answers in interval notation. seperate multiple intervals with a comma. Determine where the function is concave up and concave down. Enter your answers in interval notation. seperate multiple intervals with a comma. Enter the x-values of any local minima, maxima, and inflection points. seperate multiple intervals with a comma.

Q: At which point/s (value/s of x) is the function neither continuous nor differentiable? DO NOT…

A: see below the answer and explanation

Q: Give examples of functions producing every possible output in the last component (i.e.…

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Q: -5 0. 10 -2 5. 2.

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Q: Write a function rule for the area of a triangle with a base 3 cm greater than 5 times its height.…

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Q: Determine if the function is odd, even or neither * x2-1 x²+1

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Q: Is this a function? Yes or no

A: our objective is to conclude

Q: Should I simplify a quotient function before finding its domain?

A: No, we have to find domain first then simplify the rational function or quotient function . If we…

Q: Determine a function that will best match the following points: (1/2, 0), (2 ½, -2), (4 ½, 0), (7 ½,…

A: We find the Lagrange interpolating polynomial. We have: x x0=12 x1=212=52 x2=412=92 x3=712=152…

Q: Find the Domain of a Function Defined by an Equation

A: Consider a function in the equation form y=x3+x+8 or fx=x3+x+8

Q: ⑥, y=14x-5 x-2x+3) 5

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Q: Find the domain of the following Function- no simplifying.

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Q: Use the graph of f to Explain why f represents the graph of a function, Where applicable, use…

A: Given: To determine: Why graph of  f represents  a function.

Q: Xe is a power function true or false

A: A power function is in the form of f(x) = kx^n, where k = all real numbers and n = all real numbers.

Q: Select all relationships which represent y as a function of x.

A: (a) “It is known that; a function is a relation in which each element in domain mapped to exactly…

Q: In a few sentences explain how would you show a function is discontinuous.

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Q: 7. Give two reasons why a function might not be differentiable at a particular value of x.

A: topic -derivative

Q: x = 0 is not a function. Select one: True False

A: A function is defined as the relationship between an input and an output. In function each input…