Given that f(x) = 2x^3+9x^2-60x+70, Find the local maximum and local minimum for f(x)

Q: Consider the function f(x) =x^4 -50x^2 + 7, -4 < x <11. Find the absolute minimum and maximun of…

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Q: what is a cubic plolynomial function in standard form with zeros -4, -5 and 4 a.…

A: given zeros -4,-5 and 4

Q: A quadratic function is defined by f(x) =x^2+(k+2)x-12 where k is a constant. It is given that the…

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Q: Find all zeros for... F(x)=2x^3+3x^2-20x

A: Here is the solution

Q: Use the functions f(x) = 2x^2+1 and g(x) = 3x+5 to evaluate the composite function. f(g(2))

A: g(x) = 3x + 5 So, g(2) = 3×2 + 5 = 11

Q: Describe the end behavior of this function f(x)=(x^3)-(4x^2)+6

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Q: Let g(x) = x^2 - 3 and h(x) = 2x + 5. Find h(g(x)).

A: topic - composite functions

Q: Consider the function f(x) = 2x^3 - 5x^2 + 3x + 1. Determine the value of x for which f(x) has a…

A: To determine the value of x for which the function f(x) = 2x^3 - 5x^2 + 3x + 1 has a local maximum…

Q: Determine the real root F (x)=26+85x-91x^2+44x^3-8x^4+x^5 Graphically

A: . The real roots of an equation are the x-intercepts of the graph.

Q: Find f(x) - g(x) when f(x) = 2x^2 - 4x g(x) = x^2 + 6x   x^2 - 10x   3x^2   3x^2 + 2x   x^2 + 2x

A: In a polynomial expression, the like terms are the terms with the same variables and exponents.

Q: Consider the function F(x)= (x+2)^2 for the domain [-2, ∞)

A: Given           Function is :                            F(x)=(x+2)2 for the domain [-2, ∞)   To…

Q: Use f(x) = -2x^3 - 3x^2 +120x + 250: Find the relative maxima and minima of f(x)

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Q: Differenciate F(x)=^4sqrt(7+5x+x^4)

A: We have to differentiate the given function

Q: Given f(x) = 3x^2+4 and g(x)=-3x, calculate f(g(x)). Show all work

A: Given Function, f(x)=3x2+4g(x)=-3x We have to find, f{g(x)}=?

Q: Let f (x) = 2x + 7 and g (x) = 3x^2 + 2 Find f(g(3))

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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.