Question Suppose we have two functions f(x) and g(x) over the interval (-2, 2] such that f'(1) = 2 = g'(1). Then f(x) = g(x) + C for some constant C. Select the correct answer below: True False

Q: et f and g denote differentiable functions. If f'(x) = g (x), then f(x) = g(x).

A:

Q: Find all functions f so that f'(x) = 7x2 – 7/x. (Use C to represent an arbitrary constant. Remember…

A: We have to take anti derivative to solve  for f(x)

Q: Consider the following functions: f(x) = 4 – x², g(x) = 7x + 2 and f + g ()(-1). X-4 h(x) = Evaluate…

A:

Q: How are the functions f and g given by f (x) = (1.05)ª and g (x) = eº.05z similar? How are they…

A:

Q: If f(x) = 3 tan 1 x, then find the value of f'(5) is . %3D -5 26 3 26 3 26 26

A:

Q: 0<x<1 Q.2 Consider the function f(x)= Find x, 1<x<2 and sketch the odd and even extensions for f(x)…

A:

Q: Find the derivative using the chain and power rules. sin3x Please justify and explain why.

A: Let y=Sin3x.

Q: 2 4) Given the function f(x) = x + 1 a) Fill in the table below with the inputs and outputs of f(x):…

A: we have to find

Q: Let F(u, v) be a function of two variables. Let Fu(u, v) = G(u, v), and F„(u, v) = H (u, v). Find…

A: Given that  F(u,v)  be a function of two variables such that  Fuu,v = Gu,v  and  Fvu,v = Hu,v (a)…

Q: Assume that the function f is continuous and strictly increasing on the interval [15, 26] with f(15)…

A: Given that:               f is continuous and strictly increasing on the interval  [15,26] with…

Q: 1. Find f'(x), f"(x), and f(x) for the following functions. a. f(x) = (2-3x)5 b. f(x) = 2¹2 +324 c.…

A:

Q: 3. Consider the following table of values for two functions f and g: X 1 2 3 4 f(x) 2 4 1 3 f'(x)…

A:

Q: At what value of x does the function f(x)=x' -3r? -9x change from deceasing to increasing? 1 -1 Find…

A:

Q: x + 4 6. Let f(x) find the following: x - 3 a) f(2) b) f(4) c) domain of f

A: Use the value of x for finding the function.

Q: f(a) = ca + 4 if a E (-∞, 2] I ca -4 if a e (2, 00) if a E (2, ∞)

A:

Q: Suppose that the functions q and r are defined as follows. q (x) = -2x+2 r(x)=x² Find the following.…

A:

Q: For f(x) = S2x 3 for x < 1 for x ≥ 1 )' the value of 6 f(x)dx is

A:

Q: 1.) f (x) = 10x10 4.) f (x) = %3D 2.) f(x) = x² – 9 5.) f(x) = 2x² + Vx 3.) f (x) = –x5 – x-3 – - x

A:

Q: es. there 7. Let f(x) = x4. a) Determine f-¹(x) b) Determine f(f-¹(x)) c) Determine f-¹(ƒ(ƒ˜¹(x)))…

A: According to bartleby guidelines I can answer only first three subparts of a question.  If you want…

Q: Pleased show step-by-step

A: The given function is

Q: Determine the second derivative of 2x+ y-- 4 y 6.x (y + 2)--9(y+2) A B - 6x (y+ 2)-+ (y + 2) - 6x (y…

A:

Q: a) If h(x) = (f +g)(x), find h' (0). b) If h(x) = f(x)g(x), find h' (1). c) If h(x) = (x) find h'…

A: Derivative

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.