b) Let f(x) = ax + Bx +y be a function defined on the closed interval [a, b] where a, B,y, a and b are real constants. Is the Mean-Value Theorem applies for the unction f(x) on [a, b]? If yes, then find the value(s) of the constant(s) C. %3D

Q: Show that the function f(x)=x' satisfies the hypothesis of the Mean Value Theorem on the interval…

A:

Q: Determine whether the Mean value theorem applies for the function f(x)= 3x³+2x+3 over [0, 3 and find…

A: Verify the mean value theorem and find c

Q: Explain why the Mean Value Theorem does not apply to the function f on the interval [0, 6].

A: To satisfy the criteria of mean value theorem the function must be continuous in the closed interval…

Q: Verify the Mean value Theorem for the function f(x) = 2x2 - 8z +6 on [1, 3]

A: f(x)=2x2-8x+6  on [1,3] conditions of mean value theorem: i) f(x) is continuous at (a,b) ii) f(x) is…

Q: Use the Mean Value Theorem to show that there is no function f satisfying f(0) = 0, f(9) = 5, and…

A: If function continuous on a,b and differentiable on a,b such that fb≠fb Then f'c=fb-fab-a

Q: The value of C obtained when we apply the Mean Value Theorem for f(x) 32x2 +3 on the closed interval…

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.