Consider the function on the interval (0, 2л). f(x) = 2x + 4 sin(x) (a) Find the open intervals on which the function is increasing or decreasing. (Select all that apply.) Increasing: (0,25) (², 4) (47, 2x) none of these Decreasing: 0 (0, ²) (²,4) 0 (4,2) none of these (b) Apply the First Derivative Test to identify all relative extrema. relative maximum (x, y) = ( relative minimum (x, y) = ( (c) Use a graphing utility to confirm your results.

Q: Let f and g be functions of x, where a is an unknown constant. What is a valid expression for (-)'…

A:

Q: Consider the function f(x)=x2+6(5x−10)(x+4)f(x)=x2+6(5x-10)(x+4). For each prompt below, if no…

A: We need to find asymptote and intercepts.

Q: Let f and g be functions such that f(0) = 18, f '(0) = 3, f(18) = 11, f '(18) = - 5 and g(11) = -…

A:

Q: Find a formula for the exponentail function passing through the points (-2,40) and (1,5)

A: The general equation for an exponential equation is  y = a(b)x

Q: Differentiate the function f(x) =x*(1– 4x²)³. Express your answer in simplified, factored %3D Torm.

A: We can find the answer as below.

Q: 4(a). Define the zeroth divided difference by f[x,]= f (x; ). Write the expressions for the first…

A: As many questions are given and its various subparts, I will solve only the first. Zeroth divided…

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: Determine whether f(x)=sinx+cosx is an odd or even number

A: Given function is f(x)=sinx+ cosx

Q: find the interval where the function is increasing or decreasing  f(x) = 6/x-4

A: Function is not defined at x=4  there are two intervals where the function is defined   ( -∞,4 ) and…

Q: A function f is defined by Ax + 5 f(x) 6x - 2 If f(1) = 4, find A.

A: Given: fx=Ax+56x-2  ……1   and, f1=4  ……2   To find: A

Q: If f(x) = ax , show that f( - x) = 1 / f(x) .

A: We have to show that: f-x=1fx Where given function is fx=ax. Taking LHS (putting x=-x in fx ), we…

Q: Plot the graphs of f(x) = x(x - 3) (x + 3) and g(x) = cos 2 x together on the same set of axes and…

A: In the question it is asked to draw diagram for f(x)=x(x-3)(x+3). Also it is asked to draw…

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

A:

Q: Suppose f and g are one-to-one functions such that f(2) = 7, f(4) = 2, and g(2) = 5. Find the value,…

A: We have given functions f and g are one-to-one. Then, a. gof-17=gf-17=g2=5 b. fog-15=fg-15=f2=7

Q: Find f if f"(x) = 4 – 6x, f(0) = 3, and f(2) = -2. %3D Answer: f(æ)

A:

Q: Assume that the function f is a one-to-one function. (a) If f(5) = 2, find f-'(2). Your answer is…

A: Given that to he function f is one-to-one function.

Q: i just dont get this or functions.   Let f(x) = 2x 2 + x, g(x) = 1 − 2x, h = {(0, 1),(1, 3),(5,…

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Q: vertical asymptote(s): horizontal asymptote(s):

A: Since multiple subparts are asked, I am answering first 3 subparts