Which is the most accurate table for the derivative function f'(x)? f'(x) f'(x) -3 -3 2.7 7 3 5.4 3 4.5 4.2 4.5 -8.5 6 -4.1 f'(x) f'(x) -3 -3 1.4 -1.7 3 3 4.5 -1.7 4.5 1.4 6 -4.1 -4.1

Q: Distinguish Between Partial Derivative and Ordinary Derivative ?

A: ## Distinguish  Between Partial Derivative and Ordinary Derivative....

Q: What is the First Derivative Test for Local Extreme Values?

A: What is the First Derivative Test for Local Extreme Values?

Q: Find the Equation of tangent line of the function f(x)=1+csc(x)-√cos(x) at the point…

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Q: Find the derivative of the given function. Infsech(x) + tanh(x)) 1) sechx+tanhr sinhx+1 sechx-tanhx…

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Q: What are the the mean value theorem in application of derivatives?

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Q: 2. If the derivative of an accurately determined function is replaced with a finite difference, how…

A: Since you have asked multiple question, we will solve first one for you. If you want other question…

Q: Determine the second derivative of f (x)= x 'e* at x = -2 with a step-size of h=0.50 using Central…

A: We have to find the second derivative of the following function at x=-2 with step size h=0.5 using…

Q: Find the points on the graph of f where the tangent line is horizontal. tangent line is 3x^2-16…

A: The tangent line is horizontal where y'=0

Q: Find the derivative of f(x) at the designated value of x (Using Derivative Rules). 3 11. f(x) = x*,…

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Q: What is the derivative of f(x)=3cos(x)+2sin(x) at the point x=−π

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Q: Determine the intervals along the x-axis on which the derivative in Figure is positive.

A: The slope of a tangent line for a function at a point is the value of the first derivative at that…

Q: Which functions have a negative first derivative for all x?

A: Which functions have a negative first derivative for all x?

Q: Suppose that the function y in the Derivative Product Rule has a constant value c. What does the…

A: Derivative product rule:The derivative product rule for the functions x and y is given by,

Q: Find the derivative of the function by the limit process. f(x) = 6/x^2

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Q: If the derivative of f is f'(x) = (x – 1)(x + 2), then f is decreasing on (-2, 1) Select one: True…

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Q: A continuous function has a derivative at every point in a given interval. True or False?

A: function is differentiable means that function is continuous as well as smooth at every point of…

Q: Find the derivative of the function by the limit process.

A: Consider the function, fx=12 The limit definition of the derivatives of a function is given by the…

Q: Find the relative extrema using first derivative test   f(x)=(x-2)^6

A: Consider the function f(x)=(x-2)^6

Q: Compute the derivative of f(x)= (ex2 +e-x2 )/(ex2 -e-x2 )

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Q: Find the derivative of the function by the limit process. f(x) - f'(x) =

A: The given function is f(x)=4x2We have to find the derivative of f(x).

Q: can explain for me what is Applications of Partial Derivative ?

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Q: The second derivative of a function is equal to 1. If the graph of the function passes through (0,2)…

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Q: find the derivative of f (x) at the designated value of x. f (x) = 1/x at x = 2/3

A: Given: f(x)=1x To find the derivative at x=23

Q: Explain why a positive derivative on an interval impliesthat the function is increasing on the…

A: On an open interval Suppose  is a function on an open interval  that may be infinite in one or both…

Q: show that the function is derivable and that the derivative is continuous.

A: The objective is to show that the given function is derivable and the derivative is continuous.…

Q: What is a higher-order derivative?

A: We create, or derive, a new function f'(x) from a function f(x) called as derivative of function…

Q: Find relative extrema not using the first derivative test   s(x)=x^4-2x^2

A: We will use the second derivative test. But the route to second derivative passes through the first…

Q: Suppose the derivative of ƒ is ƒ'(x) = x - 3.a. Find the critical points of ƒ.b. On what intervals…

A: We have to find: a. critical points of fb. On what intervals is f increasing and on what intervals…

Q: Find the derivative of the function using chain rule. f(x) = esin?x

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Q: 2. Use an example to show how to use the First Derivative Test for critical points

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Q: Calculate first, second, and third derivative values for function, f(x) = -x2 + 5x + 3 at points x =…

A: Forward difference Consider a linear interpolation between the current data value (t0,I0) and the…

Q: Find the derivative of the function f(x)=1/x using limit definition derivative

A: According to the given information it is required to calculate the derivative of the function using…

Q: What

A: The correct option is (B).

Q: What is the rule for calculating the derivative of a composite of two differentiable functions? How…

A: Let us we consider a function which is real valued function which is composite of of two functions…

Q: Find the derivative of the function by the limit process. f(x) = 7

A: The given function f(x)=7. The derivative of the limit  for the function f(x) is defined by So, to…

Q: Find the general anti-derivative of f(x) = 3. + Vx on a continuous interval. Please select file(s)…

A: topic - integration

Q: Find the derivative of a composite function using the Chain Rule or General Power Rule.  1.) y=…

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Q: If a function is increasing everywhere (and it has a derivative), then it's derivative function is…

A: explanation of above question is given below,

Q: Find the derivative of y 3 sin x +5 cos x A. 3 cos x +5 sin x C. 5 cos x +3 sin x B. 3 cos x-5 sin x…

A: Differentiate wrt x

Q: y = x-12; (4,) Use the derivative feature of a graphing utility to confirm your results.

A: We will solve the following

Q: Find the derivative of the function at Po in the direction of A. f(xу) 3 - ху- Зу?, Po(-7,0),…

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Q: If the average rate of change of q (x) in the period (5,7) is equal to 8 and y (5)*y (7) = 16 and f…

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Q: Find the derivative car (x+y) = yrinx

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Q: Find the derivative of the function f(x) = csch () () -2 coth csch 2 2 -2x coth csch -x coth csch 2…

A: L

Q: Find the derivative of f(x) at the designated value of x (Using Derivative Rules). 3 11. f(x) = x*,…

A: Given :   f(x)=x4 , at x=3/2 f(x)=1/4 , at x=2

Q: Find the derivative of the function at Po in the direction of A. txу) - - ху + у, Р,(10, - 2),…

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Q: How do you find the derivative of the quotient of two functions that are differentiable at a point?

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Q: What is the definition of the derivative (Difference Quotient)?

A: 2. What is the definition of the derivative(difference quotient)? ans. In single-variable calculus,…

Q: A function at x=2.1 , 2.2 , 2.3 has values 22, 18 , 16 respectively . the most accurate first…

A: the values f(2.1)=22,f(2.2)=18 and f(2.3)=16 the derivative…

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.