[5] Let f(x) = 3xe" – cos x. Use the following data and the Second Derivative Midpoint Formula to approximate f"(1.3) with h = 0.1 and with h=0.01. 1.20 1.29 1.30 1.31 1.40 f (x) | 11.59006 13.78176 14.04276 14.30741 16.86187 Compare your results to f"(1.3).

Q: What is the derivative of y = cos² x?

A: According to the chain rule of differentiation:

Q: Pictured above is the graph of f', the first derivative of a twice differentiable function, /(x), on…

A:

Q: Find the first derivative at x 2 for the function given by the data 1.0 1.5 2.0 3.0 0.4057 0.69315…

A: By the finite difference method f'(x)=f(x+h)-f(x-h)2h                [Second order approximation]

Q: I need  a and b both answer

A: We need to use nearby data points to approximation the derivative in order to estimate the second…

Q: Use the graphs of f and g, shown below, to find the following. yA 4. ((2). If the derivative does…

A: Write the derivative of the form u/v then substitute the value of x at which we have to find the…

Q: Find the derivatives of the following functions with respect to x  x=tan (e-y)

A:

Q: The derivative of the given function below is: f(x) = cos¬'(3x) sin-(x²) 2sin-(x²), 3xcos-(3x)…

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.