For f(x) = 2x-4x2 +8 find the following. (A) f'(x) (B) The slope of the graph off at x= -2 (C) The equation of the tangent line at x= -2 (D) The value(s) of x where the tangent line is horizontal (A) f'(x)=] (B) At x= -2, the slope of the graph of f is nt (C) At x = - 2, the equation of the tangent line is y= . sS (D) The tangent line is horizontal at x =I- (Use a comma to separate answers as needed.) SS

Q: Find f.   f ''(x) = (5/6)x5/6

A: Consider f''x = 56x56

Q: The revenue (in billions of dollars) from artificial intelligence for enterprise applications in a…

A: The revenue from AI for enterprise applications in a country for the year from 2016 to 2027 cab be…

Q: 4 -4 -3 2 4 -2

A: See from the given graph of the function fx, the graph becomes parallel to x axis at the points x=-2…

Q: Starting with the graph of f(x) = 9", write the equation of the graph that results when: (a) f(x) is…

A: f(x) = 9x a) f(x) is shifted 7 units downward, y = (9x - 7)

Q: If f(2) = 3 and f '(2) = -1, find the equation of the tangent line when x =

A:

Q: Complete the following. f(x) = 3x² - 7x + 25-24 at x = 4 (a) Find the derivative of the function and…

A:

Q: Ay Use the given graph of y = f(x) to evaluate the following. (a) f(-3) (b) f(2) (c) f(0) (d) f(-3)…

A:

Q: Write an equation of the tangent line to the graph of y = f(x) at the point on t -10x2 - 3 12) f(x)…

A: Explanation of the answer is as follows

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.