4) Where is the function g(x) = 3x2 -x+ 5 differentiable?

Q: aximum v al [1, 5] is

A:

Q: Let f(x) = 4x + 1 f¹(x)

A: Given query is to find the inverse of the function.

Q: 5. Let f(x) = x² + 3x and g(x) = 2-x. (a) Find (f - g)(x) (b) Find (fg)(2) (c) Find (4) (x) and its…

A:

Q: 6) Differentiate: a) f(x)= 5x-3 +1)

A:

Q: Enter an eqvation_for the line of symmetry for the function flx)=4x²+[6X-9 %3D

A: The function is given by f(x) = 4x2+16x-9 To evaluate : Equation of the line of symmetry

Q: 10. Differentiate each function. a) y= -3x² + 4x – 5 b) f(x)=6x¬1- 5x=2 O f(x)= 4Jx

A:

Q: The domain of the function f(x)=√12+4x−x^2 is the closed interval [A,B] where A= and B=

A: Domain is the set of all values that can be taken by x so that the equation is defined.

Q: If f(x)=(3m-2)x+6 is a constant function m =?

A: For the constant function the coefficient of x should be zero.

Q: Differentiate the function f(x) = In(6x7 – 4x) + v2 – e3x. - -

A:

Q: f(x) = −x^2 + 8x − 16. Consider the Parabola (a) Does the function point up or down? (b) What is…

A: f(x)=-x2+8x-16y=-(x2-8x+16)y=-(x-4)2 a. parabola is down to the axisb.symmetric to x-axisat x=4

Q: f(X) = 2/X       g(X) = X+1/9     (What is the domain?)

A:

Q: Let f(x) = 9x + 12 ƒ-¹(x) =

A: Solution:

Q: Find the point of f(x) = 2x3 - 9x2-17x - 3 is at [0, 00) on which concavity changes. %3D

A: We draw graph of given function.

Q: 4) Suppose that x thousand units of a product will be sold when the price is p(x) = -2x + 31 dollars…

A: Please see the explanation below

Q: Find f(g()) and g(f(2)) for the pair of functions. f() =+1 g(2) 34x-17 flo(2)) = %3D 9(f(=)) = %3D

A: Given, f(x) = x + 1  g(x) = 4x - 17

Q: Explain how f (x) = (x − 1)2 + 3 is obtained from f (x) = x2.

A: Given f(x)=x^2, to obtain f(x)=(x-1)^2 from f(x)=x^2 we have to shift the graph to 1 unit right.

Q: f(x)=2-\x t4| give their domain, range, -intercept, and y-intercept

A:

Q: f(x) = x* + x³ – 2x² What is the domain of the function given above?

A: We have to find the domain of the given function

Q: b\ Find the domain of the functions: (1) y = (2) y = = (3)f(x) =

A:

Q: Explain why f(x) satisfies the Intermediate Value Theorem. f(x)=ex - x3 - 8

A:

Q: 5) For functions f (x) = x² – 15x + 45 and g(x) = x - 9, find |(x)

A: f(x)=x2-15x+45, g(x)=x-9, (fg)(x)=?f(x)=x2-15x+45  g(x)=x-9  Now fgx=f(x)g(x)             [Quotient]

Q: I need to find f"(x) when f(x)= (x2+10)6

A:

Q: fl-8)== y= 3/x at point (-8;2) %3D m =

A: We are given the function f(x)=x3. Here,               f(-8)=-83=-2. Now, we need to find Slope of…

Q: Let f(x)=x^2-6x+9. Find x such that f(x)=1 The solutions are nothing

A: First I have set the polynomial equal to 1  That is set,  f(x)=1 and solve for x, we get x=2, X=4

Q: Consider the function f(x) =(x +1 )( x-1)² 16. What is the inflection point?

A:

Q: Let f(x) = 6x + 6 ƒ-¹(x): =

A:

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.