The graph of f(x) is shown below as a blue curve and y=X as an orange dash line. Input the two points that correspond to f^-1(-3) and f^-1(8).

Q: What is the slope of the line tangent to the graph of a function defined by f(x)= 2x²-4x+5 at…

A: f(x)=2x2-4x+5Let y=2x2-4x+5Differentiate

Q: Find the higher order derivative  f'(x)=7x2-9x2+4x f'''(x)=

A: We will use the following : ddxxn = nxn-1 ddxc = 0 where c is constant.

Q: Describe geometrically when a function typically does not have a derivative at a point.

A: To describe geometrically when a function typically does not have a derivative at a point.

Q: Find the derivative of the functions f(x)=(2x2-1)(x3+3)

A: We can make it easier for you.

Q: FInd the derivative of y=(5x-3)5(2-x4)5

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Q: Find second derivative of f(x) = 7x-15

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Q: Graph f(x) = x +2x -5 and the tangent line to the graph at the point whose x-coordinate is -2.

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Q: Describe the Chain Rule for the composition of two differentiable functions in your own words.

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Q: f(x) = 6x3 - 9x + 4 +4

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Q: How to use a graph of a derivative to determine the parent function.

A:

Q: Find the derivatives of the functions in Exercis y = (4x + 3)4(x + 1)-3

A: y=(4x+3)4(x+1)-3

Q: Find all functions ƒ whose derivative is ƒ'(x) = x + 1.

A: Given that f'(x)=x+1

Q: What information about a graph can be found from the second derivative?

A: What information about a graph can be found from the second derivative?

Q: Explain how to write an equation of the tangent line to the graph of f(x) = x2 at (2, 4).

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Q: What is the second derivative of: -(4-x^2)^1/2

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Q: Find the derivative of sech(2x1/9)

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Q: he figure shows the graph of the derivative f' of a function f. yA y= f'(x) -2/

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: find the derivative of the function F(x)=4(x^3-x)^4

A: According to the given information, it is required to find the derivative of the given function.

Q: 5, i, Evaluate the first and second derivatives of the function z-2x4+3x3+2x-5 when x = 4.

A: We have to find the first and second derivative of the function z=2x4+3x3+2x-5 when x=4.

Q: Find the critical points and apply the Second Derivative Test (or state that it fails): f (x) = x5 −…

A: f(x)=x5-x3

Q: Find the derivatives of the functions in Exercis y = (2x - 5)-1(x2 - 5x)6

A: Given function - y = 2x-5-1x2-5x6y = x2-5x62x-5               ........(1)  Identity to be used -…

Q: Find an equation of a line that is tangent to the graphof f(x)= x3 -3 and Perpendicular to the line…

A: If two lines are perpendicular then product of their slope is -1. m1.m2= -1 Equation of a tangent…

Q: How can the derivative function definition be applied to this problem?

A:

Q: What is the second derivative of the function:  f(x) = (9x^2)/ (x^2-49) Please show ALL steps

A: Given function is

Q: Find derivative of f(x)=2x-7

A:

Q: f(x) =  3 − 3x − x2 x2 − 5  f '(x) =

A:

Q: Find third derivative of  f(x) = 6x^2-7x+8

A: We have to find third derivative of  f(x) = 6x2 - 7x + 8 The first derivative of f(x) is  f'(x) =…

Q: Find the derivative of the function. f(x) = arcsec(4x) 4 f'(x) = 4√ 16x²2 - 1 or 1 x√ 16x² - 1 X

A: As we know that the derivative os sec inverse x is: ddxsec-1x=1xx2-1

Q: What rule should be used in getting the derivative of y=(1−x^2 )^6

A: What rule should be used in getting the derivative of y=(1−x^2 )^6

Q: Find the derivative of the function by definition. 1- V2x+3

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Q: Graph f(x) x'- 3x-9x + 2. 3r2

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Q: Find the function of the derivative f'(x)= -12x+5 and with the graph passing through (-2,5)

A: Given, f'(x)= -12x+5

Q: Find the derivative off (x) = 9x - 5 at x = 2 and x = 5.

A: Given f (x) = 9x - 5

Q: Find the derivative of (x-x^4)/(7/x^2+6/x^3)

A: Formula used:

Q: FInd the derivative of  y=(3x-2)2(5-x5)4

A: Assume u=(3x-2)2 and v=(5-x5)4 Differentiate the function u with respect to x. Assume p=3x-2…

Q: derivative of f(x)=2x^15-3^x, f^15(

A: We will find the required.

Q: Find the second derivative of f(x)=x^-2 when x=4

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Q: 5. Sketch the graph of y = x3 + 5x2 + 3x - 4 by using the properties of the derivative.

A: Find f' (x) then we check f(x) increasing Or decreasing.

Q: Find the derivative of f( x ) = x^9log5(x+5.5) f'(x)=

A:

Q: Draw the graph with the first derivative

A: Draw the graph with the first derivative

Q: Find the function with the given derivative whose graph passes through point P. F'(x)=2x-3, P(5,5)

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Q: What information can be obtained from derivatives? Please provide 2 examples from the real world and…

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Q: Find the derivative of the function without using the Quotient Rule. 4x -27 y' = ( 4x10)

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Q: Explain derivatives on optimization ?

A: Topic:- derivatives

Q: State the second-derivative test for functions of two variables.

A: State the second - derivative test for functions of two variable.

Q: What is the derivative for: X^3/(1-x^4)

A: What is the derivative for  x^3/(1-x^4)

Q: The first derivative of the function f(x) is given by its graph.. f'(x) 3- 2-

A: A.  Function is increasing when f'(x) > 0  from graph  Function is increasing…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.