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: Find the domain and range oT . f(x) = 1 i) f(x) = ii) x-1 1+vx

A: Given: fx=xx-1fx=11+x

Q: (a) f(x) = F(x, 2): then ƒ'(x) = (b) f(x) = F(4,x): then f'(x) = (c) ƒ(x) = F(x,x): then ƒ'(x) = (d)…

A: Total derivative of function z = f(x, y) is given as dz=∂z∂xdx+∂z∂ydy We are allow to solve first 3…

Q: (c)f(x) = x+1 (d) f(x) = log,x, b>1 %3D >

A:

Q: Question number 2.

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: 12 If f(x) = todt then f'(x) =

A:

Q: 7 -7 Use the fact that the derivative of the function f(x)= is f'(x) = - to find the equation of the…

A:

Q: You are given the following equation & information.  ln (1+y) - ln y = ln (x3 + 1) - 2 ln (x - 1)…

A:

Q: 3 The graphs of several functions f(x) for which f'(x) = - is X shown. Find the expression for the…

A: Given f'(x)=3/x and f(x) passes through the point (1,4).

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: 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: Which interval is f increasing when f' (x) = x- x? (a). (-o, 0) (b). (-1,0) (c). (–1,1) (d). (0, 0)…

A:

Q: You are given the following function. 4t G(t) t + 9 (a) Find the derivative of the function using…

A: We will use the quotient rule of differentiation to find the derivative of g. While finding domain…

Q: Let f be a function defined on the closed interval -4sxs4. The graph of f', the derivative of f, is…

A: Let's find.

Q: Determine the signs (positive, negative, or zero) of y = f(z) (shown in graph) and f'x) and f"(z)…

A:

Q: You are given the following function. 10t G(t) = t + 7 (a) Find the derivative of the function using…

A: The objective is to find the derivative of the function using definition and find domain of G(t) and…

Q: 13. Question: If f(x) is a position function, how could we describe f'(x) and f"(x)?

A: we have f(x) as positional function.

Q: If F'(x) = f(x) and F(0) = 0, find F(b) for b = 3, 5, 7, and 9.

A: Given graph of f(x)

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

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

Q: x²-4 if x<2 Let f(x)={ x – 2 cx-8, if x2 2 For what value of the constant c is the function f…

A:

Q: Suppose h(x) = x² - 4x³. Which one of the following is true? Select one alternative: ○ The first…

A: If the derivative of the function is positive in a interval then the function is increasing And If…

Q: Consider the function defined by f(x) = -x + ae"-1, where a e R: (1) find a such that the graph of…

A:

Q: Let f(x) = 1 and 1 if x > 0 g(x) 8 +- if x < 0 Show that f'(x) = g'(x) for all x in their domains.…

A: Given,The function g(x)=1x Consider only the case when x&lt;0 because already know that f(x)=g(x)…

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.