( 2x +7 x<1 10-5x x21' 5. For the function defined by f(x)= , which of the following represents the value of f (2)? (1) 1 (3) 10 (2) 11 (4) 0

Q: Find f(-1) + f(4), given the function: 14 11 04 13 x² + 1, if x 1

A: Topic = Functions

Q: 3. If f(x) = x + 1, find f(3) and f(- 3). Is f a one-to-one function?

A: The given function is fx=x2+1

Q: f(x) = -7x + 6 x² +6 if x < 0 if x 20

A:

Q: For fx) = x+6, find each of the following a. (-1) e. (for xs97) (5) a. f-1)-5 b.r (5)-0

A: Given query is to find the indicated valen do the function.

Q: Determine which of the following functions are valid PSDS (i) wó + 30 +3 (ii) exp|- (@- 1)

A:

Q: For the following function:{x^3 if − 2 ≤ x &lt; 1{3x + 2 if 1 ≤ x ≤ 4find f(−1), f(0), f(1) and…

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Q: Evaluate the following function. If p (x) = 7 (4)" , find p (5)

A:

Q: Question 9 Ay f (x) =< ; Estimate f (-2) %3D 8-6 4 O -1 -2 O None of these 2]

A: The graph of the function crosses the x-axis when x=-2. Then, the value of the function at x=-2 is…

Q: Assume that f is a one-to-one function. (a) If f(1) = 8, find f −1(8). (b) If f −1(3) = −9, find…

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Q: Given the following function, find f(x) where (-1,6) is a point on the graph of the function.

A:

Q: Find the ranges of the following functions: f (x)= 4* – 2* +1

A: Rnage of the function f(x) is the value of f(x) for x where f is defined.

Q: 6- Do a complete analysis to sketch the following function. F(x)=2x-x²/x²-2x+1

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Q: Refer to the function below and evaluate it where f (7). /(t) = -3 (-3 ( +-1))' + -1

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Q: 1 Compute and simplify the difference quotient for f(x) = V1- x

A: The given function is fx=11-x. Replace x by x+h and obtain that, fx+h=11-x+h. Obtain the difference…

Q: Use the tables for functions f and g to evaluate each. f(x) g(x) (f - 9)(6) = f(-5) = -5 -3 4 2 1 -5…

A:

Q: Determine h(x²) for the following function. 3x h(x) = %3D x2 + x- 6

A: Solving the problem by jus finding the value of h(x2).

Q: Evaluate the following function. If p (x) = 4 (3)", find p (3)

A: p(x) = 4(3)x to find p(3) we will put value of variable x = 3 .

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.