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

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

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

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: 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.