1. Consider the function f: [-3, 2] → R defined by f(x): = x² + 4x when 3 x < 0; -x³ + 9x² - 15x when 0≤x≤ 2. A. Does the Extreme Value Theorem apply to function f? Why or why not? B. Despite the fact that the equation -3x² + 18x - 15 = 0 has a solution when x = 5, function f does not have a critical point at x = 5. Why? C. Find all critical points of function f. D. Find the minimum and maximum values of function f.

Q: Let m(x) = 2x² - ax - 2 and n(x) = bx² + 2x + 5. The functions are combined to form the new function…

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Q: O a. La función no tiene punto de inflexión. b.x = 1 & X = - 1 O.c.x = 1 d.x = - 1

A: We can find the inflection point as below.

Q: 4. Find the Factors of the function. f(x) = x* - x³ +3x? -9x-54 zero: x = 3

A: Given query is to find find the factors of the expression.

Q: 4) Write the following functions in vertex form. 2 a) P(x) = x 2x - 7 b) P(x) = - - x² + 6x + 2

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Q: 3. a) Determine algebraically whether the function f(x) = –3x° + 4x² is even, odd, or neither. b)…

A: Please find attachment for the details solution

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A: In our function three expression added together. Hence we going to see each expression separately…

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A: given  f(x)=-2x2+3xfor domain  x2+3x≠0

Q: Suppose f(x) = 2x² + 6x + 2. Compute the following: A.) f( – 3) + f(1) = B.) f( – 3) – f(1) =

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Q: Given that f(x) = 4x² + 5X-9, find f (h-3)-f(-3) h

A: f(x)=4x2+5x-9for f(h-3) put h-3  in f(x)

Q: 8) Find 4 given : f(x)=- (3x² – 2x +1)'

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A: Given, f(x)=x2-4xg(x)=2+x To find: fg(-3) Note that fg(x)=f(x)g(x)

Q: Let F(a) be Z2. Show that a2 and a2+a are zeros of x3+x+1.

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Q: 5.) Evaluate f(-3) for f(x) = x³ +3x + 17

A: Given  f(x) =x3+3x+17

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Q: 173 5. Write the domain of each of the functions in interval notation 2x a. f(x)=- b. g(x)= V1- 3x…

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Q: Showthat fo= x| is Continuous evalyuhore- 1x1+1

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Q: Find the open interval(s) on which f(x) = - 5x+ 50x +8 is increasing or decreasing.

A: Given that:

Q: 25. Let f(x) = 5x² + 1. Evaluate and simplify each of the following: f(4)-f(1) 4-1 (A) (Bu PC (B)…

A: Given function is we have to evaluate the following  and simplify them