Find the values of m and n that make f(x) continuous over (-∞, ∞): x² 4 x -2 f(x) = { mx² 2 m = n = 2x - - - 5 nx - m - n if if if x < 2 2 < x < 4 x > 4

Q: Let f(x) = 2x – 1, g(x) = 3x, and h(x) = x^2 + 1. Compute the following: A. f(g(h(2))) B.…

A:

Q: Let f(x) = 6x² + 2x³. Select all intervals where f(x) is INCREASING, (3) (0, ∞) (,0) (-∞, -3¹²¹)

A:

Q: Show that f(x) = 2/x2 + 3x4 – 5x6 is an even function

A:

Q: Show that the function f(x) = 2(x^3)-4(x^2)+5x-4 has a zero between x = 1 and x = 2.

A: Please refer to the image below

Q: For the function f(x) = 5x° -4x +2x + 3, findf "(x). Then find f"(0) and f"(4). f"(x) = Select the…

A: Double derivative

Q: f(x) = x^3 - 9x^2 - 45x - 27. Find the remaining zeros given that -3 is a zero of f(x). O (-3, -6 +…

A: Given f(x) = x3 - 9x2 - 45x - 27

Q: Differentiate the following function. y=x(x5 + 5) 3 Choose the correct setup below to differentiate…

A:

Q: For what value of k will the function f be continuous on (-, ∞)? x2 - 81 if x + -9 f(x) = X + 9 k if…

A:

Q: Use the function f(x) = 5x – 6 to compute and expand and simplify the following. a. f(-) = b. f(-6a)…

A:

Q: fx) = x-x, g(x) = 9-2r, and h(x) = x² + 2x-63

A: Given f(x) = x2-x, h(x) = x2+2x-63 To find the function (f-h)(x) By definition of the difference of…

Q: Find the values of a and b that make f continuous everywhere. b = f(x): x-2 ax² - 6x + 3 4x -a + b…

A:

Q: Given f(x)= x^3 − 6x^2+9x, find the multiplicity of the zero at x = 3

A:

Q: Let f(x) = 2x – 1, g(x) = 3x, and h(x) = x^2 + 1. Compute the following: A. f(g(-3)) B. f(h(7))…

A: I have given the answer in the next step. Hope you understand that

Q: Show that the function x- 16 - f (x) = x + 4 4 - 10 x = 4 has a removable discontinuity at x = 4.

A: A real valued univariate function f=f(x) is said to have removable discontinuity at c in its domain…

Q: Choose all functions that are members of the same family. Oy=-x(x − 3)(x + 5) Oy=x³ + 2x² - 15x…

A: By simplifying each function, we can identify the members of same family.

Q: f(x)= 23-4b            If x=3

A: Continuity: A real function f(x) is said to be continuous at a∈R (R− is the set of real numbers), if…

Q: Find removable discontinuities in f(x)=9x5-3x2+1

A: To remove discontinuity we need to factor numerator and denominator.

Q: If f(x) = 2×, show that f(x + h) – f(x) = 2×( 2" -1). h Simplify your answers completely at each…

A:

Q: Let f(x) = x + 3 if x ≥ 5, 8 if x &lt; 5. Find f(12) - f(-12).

A:

Q: Which function grows faster as O x → +∞ ? 3x¹ + 2x³ + 3x² +1 x³ ln(x² + 1)

A:

Q: Apply Corollary 2 to the Intermediate Value Theorem. f is a polynomial and continuous everywhere.…

A: Given that, f(-3) = 170 &gt; 0 f(-2) = -25 &lt; 0 f(-1) = 2 &gt; 0 f(0) = -1 &lt; 0 f(l) = 2 &gt; 0…

Q: Suppose thatf(x) = (x+ 5)^3(x-2)^4. Find the x-coordinates of all points of inflection

A: To find- x-coordinates  of all points of inflection.

Q: f(x+h)-f(x) The difference quotient is defined as where h + 0. Find m for f(x) = x² – 9

A: Difference equation

Q: The graph of function f(x) = 5x – 7x² – 8 is concave - downward on

A: For the given Function  f(X) is concave downward on (-∞, 7/15)  So none of the options is correct.