1. Assume that it costs Sony approximately C (x) = 800, 000 + 340x + 0.0005x2 dollars to manufacture x Playstation 4’s in an hour. a. Find the average cost function in terms of x. (Recall: the average cost is C(x) = C(x)/x) b. Use the First Derivative Test to identify the relative and absolute extrema (if any) of C.   part (b) continued. c. How many Playstations should be manufactured each hour to minimize the average cost per Playstatio

Q: Q1) The dervative of the function f(x)= |x+2, using the definition of derivative is 1 b)- a) x+2 x+2

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Q: 1. FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF THE FUNCTION f(x) = 5 – x² AT (3,–4).

A: f(x)=5-x2 To find the slope of tangent, we can use two alternatives (1) Direct derivative (2)…

Q: 1. Find the slope of the tangent line to the graph of f at x = 4, given that f(x) = -x2 + 4Vx.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 1. Determine the points where the slope of the tangent to the curve: a. f(x) = 1- 3x² is equal to 5…

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Q: 9) Find the equation of the tangent line to the function f(x)=-3x² - 2x at the point where x=1. Give…

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Q: What is the slope of the tangent line that touches the graph of In(y) +e-=3y– 4x at the point A В) з…

A: slope , m=dydx.

Q: 4. Write an equation for the line tangent to the curve f(x)=" In(3x) -at x=1

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Q: II. Obtain the required order or level of derivative. 1. y = 3x5 + 4x³ – 4x + 1, find y" 2. f(x)…

A: Solve differentiate

Q: Find the critical points of the following function. f(x) = 5x? - 3x – 1 What is the derivative of…

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Q: Find f(x) if f(2) = 3 and the tangent line at x has slope (x - 1)e** - 2x. f(x) = 1)et?

A: We have to find the function

Q: 2. Determine the equation of the line perpendicular to the tangent line to the function f(x) = e' at…

A: We will find the equation of the line.

Q: 4. A. Use the tangent line to find a linear approximation to the function f (x) = Vx near x = 64.…

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Q: Find the slope of the tangent line to the graph of the functiony=f(x)=−6.5x^2 at point x=7

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Q: 1) Find the equation of the line tangent to the graph of f(x) = (x² + 1)(x³ + 1) at the point where…

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Q: If f(x)=sqrt x, find the linearization L(x) at a=4. Thus the graph of L(x) would be tangent to f(x)…

A: Given information: fx=x ,  at a=4 Formula of Linearization  Lx=fa+f'ax-a

Q: Find f'(a) using the definition of the derivative at a point for: f(x). 1 = √x at a = 4.

A: Find derivative using  definition of f(x)=1x at a=4

Q: A) Find an equation of the line tangent to the function of x2 + (y – x)² = 9 at x = 1. dy 3) Using…

A: A).Givenx2+(y-x)2=9(y-x)2=9-x2y-x=±9-x2y=±9-x2+x -----{1}Taking positive of equation {1}y=9-x2+xNow…

Q: Find the derivative of the below functions: In(x) y = 1-8 In (x) y' = (a) = In(/ 5x – 7) y = INV5X -…

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Q: If the slope of the tangent line to the graph of f(x) at x is m(x) = 3x<– 2x +1 and f(2)=3, then…

A: Given query is to find the value of f(-4).

Q: Find an equation of the line tangent to the graph of the function: f(x) = V2x² – 1 at point P(-1;1).

A: Given:- f(x) = (2x2-1)(1/3)  To find:- Equation of tangent line at point p(-1, 1) on given curve

Q: Differentiate y - V3x² – 4 using the Chain Rule. 6. What is the outer function of the given problem?…

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Q: Find the slope-intercept equation of the line tangent to the graph of y = e when x = In 3. O y = 3x…

A: The given function is y=ex and the point x=ln3

Q: Find the equation of the line tangent to the graph of f(x)=(lnx)^2 at x=3.

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Q: 4. Find the slope of the tangent line to the function f(x)= +3; x+2 at x = 4 5x-10

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Q: 8) Find the equation of the tangent line to the graph of g(x) x3 7 at x = 2. -

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Q: Let y=x(lnx)^2. Find the value of x for which the second derivative y"(x), equals zero.

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Q: 1) Find the slope of the tangent line to the graph of f (x) = x3 + x at x = 3.

A: Application of derivative problem

Q: 7. Determine the equation of the tangent to the function E-2 f(x)=- at x= 1.

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Q: Suppose 8 (x) 1+ x. What is the correct result of the derivative of g with respect to ? A 8'(x)=…

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Q: If the slope of the tangent line to the graph of f(x) at x is m(x)=3x^2-x+1  and f(2)=4, then what…

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Q: Suppose h(x): . What is the correct result of the derivative of h with respect to x? 3x · In (5)…

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Q: 1. Use forward and centered difference approximation method to estimate the derivative of the…

A: Given the function is fx=x3-2x+4. The forward and centered difference approximations to estimate the…

Q: Find f(x) if f(1) 7 1 and the tangent line at (x, f(x)) has slope f(x) =

A: We know that the slope of tangent at any point to the curve of a function is given by the derivative…

Q: 2 Determine the equation of the tangent line to the graph of f(x) = Vx-12x at the point where x -3.

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Q: Q1) The dervative of the function f(x)= |x+2 using the definition of derivative is

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Q: 8) Find the equation of the line tangent to the graph of f(x) = x – :- at the point where x = 1.

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Q: Find f(x) if f(2) = 3 and the tangent line at x has slope (x - 1)e - 2x, - 2x 3 fx) 2

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Q: 12. (a) Use the definition of derivative to find the slope of the tangent line to the curve f(x) =…

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Q: What is the slope of the tangent line that touches the graph of Iny+e2x-1 = 3y – 4x at the point A 1

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Q: Find an equation of the tangent line to the graph at the given point.

A: Given, fx=4xx2+6 Now we find the slope ddx4xx2+6 Now by using the quotient rule,…

Q: Q2: A) Find an equation of the line tangent to the function of x2 + (y- x)² = 9 at x = 1. dy if y =…

A: Derivative of function

Q: 3 Find the slope of the tangent to the graph of f(x) = /x+5 at the point where x= 4.

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Q: 6. у3 In (x*+3х -1)2 V(5x+2) step1 step2

A: Derivative of function

Q: 2. Use the definition of the derivative of a function at a number to calculate f'(8) where f(x) is…

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Q: Suppose the derivative of the function y = f(x) is y' = (x-9)2(x+6). At what points, if any, does…

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Q: The graph of a function is shown together with the tangent line at a point P. y 5 4 3 2 1 2 3 4 6. 7…

A: topic- tangent

Q: 2. Determine the true error and the relative true error of the first derivative of f(x) = 2.5-* %3D…

A: Solution is below

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

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.