For the graph off (x)(graphed below), what would the value of f' (x)have on the interval 1 < x < 4? -5 -4 -3 -2 -1 1 2. 3

Q: Upoint Find the derivative with respect to x of 8. f(x) = ( (2x³ + 4)° + 6 ((2x³ + 4)* + 6)° + + 7.…

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Q: 4. Is the function given by G(x) 1 x-1 the interval (0, ∞)? Why or why not? continuous over

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Q: Consider the function f(x) whose second derivative is f”(x)=5x+2sin(x). If f(0)=4 and f’(0)=4, what…

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Q: Suppose that the tangent line to the graph of a function f at x=2 passes through the point (5,19)…

A: Given that the tangent line to the graph of a function f at x=2 passes through the point (5,19) and…

Q: Find the length of the curve of the graph of the indicated function. y = In(sen x), between points…

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Q: find the function with the given derivative whosegraph passes through the point P. ƒ'(x) = 2x - 1,…

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Q: Your job is to estimate this special base. In other words, estimate the value of b for which, at…

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

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

Q: Here is the graph of the function h(x)on the interval (-5, 5), and part of a line tangent to h(x) at…

A:

Q: Suppose that the second derivative of the function y=f(x) is y'' = (x-3)(x+9). For what x-values…

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Q: What is the derivative of the function with respect to x of (x + 1)³ – æ° -

A: Given : Function x+13 - x3   To find : Derivative of the given function with respect to x?

Q: Find all possible functions f with the given derivative. f'(x)= 1/x-1, x is greater than 1

A: Obtain the all possible functions as follows.

Q: how would you, using a limit def. of a derivative at a point find f'(-1) for the function f(x). =…

A: Hint:

Q: fx て (X)

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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: Find the derivative by the limit process. f(x) = 14-x²

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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 an equation of the tangent line to the graph of f at the given point.

A: The equation of the tangent line to the graph of f at a given point x0,y0 is y-y0=f'(x0,y0)x-x0…

Q: Find the derivative f(x)= In(ex+9)

A: find the derivative

Q: Find the derivative of the function. (x) - In(4 - x") f'(x) -

A: Find the derivative of the function.      fx=ln4-x8

Q: Find the derivative of the function by the limit process. f(x) = 5x − 4

A: fx=5x-4

Q: Match the graph of f, below, with that of its derivative. -2 -1 1 2 3 4 1- -2 4 6 -4+ -3- -6+

A: This question is related to Functions and its derivative, we will solve it using given information.…

Q: Suppose that the second derivative of the function y = f(x) is y" = x*(x = 2)°(x + 3). For what…

A: Given: The second derivative of the function y=f(x) is y"=x2(x-2)3(x+3) Definition: The inflection…

Q: Consider the function f(x) whose second derivative is f''(x)=4x+3sin(x)   If f(0)=3  and f'(0)=2…

A: detailed solution with explanation is given below

Q: Use the fact that the derivative of the function ​f(x)=4/x is f"(x)=-4/x2 to find the equation of…

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Q: The tangent line to y = f(x) at (-1,-8) passes through the point (-7,5). Compute the following a.)…

A: The tangent line to y=f(x) at (-1,-8) passes through the point (-7,5)

Q: The first derivative of the function h is given by h' (x) = x³ – 3x2 + x. What are all intervals om…

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Q: Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.

A: Consider the given: The numerical derivative does not exist a point in three cases: 1) when there is…

Q: Which of the following has a derivative of f (x) = 2x (arctanx + arccotx)?

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Q: By using the definition of the derivative find to f "(x) 3x3 +1 1 Ve +1 x +1

A: 1. We solve first order derivative of f(x)

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

A: The objective is to explain the reason definition of numerical derivative doesn't exist at x=2 in…

Q: The tangent line to the graph of a function f at the point x =2 has x-intercept 10/3 and y-intercept…

A: Given query is to find f(2) and f'(2)

Q: 1. Use the limit definition of the derivative to determine the derivative.2. Determine the equation…

A: We have to find derivative using limit definition of derivative and then find tangent line to f(x)…

Q: Consider the function f(x) whose second derivative is f''(x)=8x+10sin(x). If f(0)=3 and f'(0)=2 what…

A: The function is f"x=8x+10sinx.   Integrate the function.…

Q: What role does the denominator of f'(x) play in finding the critical points (in other words, what do…

A: The given data is: f'x

Q: The derivative of f is equal to f'(x) = f(x)f(-x). Show that f' is not one-to-one. %3D

A: First we will find 1st derivative using the given relationship.

Q: A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f, the tangent…

A: Given problem:- A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f,…

Q: f'(x) at x if f(x) = csc³(x).

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Q: Find the derivative by the limit process. f(x) = 11-x²

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Q: Find the intervals of increasing and decreasing, and intervals of concavity for f(x)=x^2/3(x-4) Do…

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Q: What is the limit that will calculate the derivative f'(2) for the function f(x)= x-1

A: solution of the given problem is below...

Q: How do I find the 20th derivative of f(x)=(2cos x)(cos 3x)? I think there must be some trick because…

A: Given:

Q: 4. By the definition of derivative prove that f(x) = √x² +5 is differen- tiable at x=2.

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Q: What is the derivative of f(x) = 1 over x⁵

A: here we use the formula of derivative  ddxxn=nxn-1

Q: Find the derivative of the function by the limit process. f(x) = x3 - 9x + 1 f'(x)

A: We know,f'(x) = limh→0 f(x+h) - f(x)h  by limit processHere,f(x) = x3 - 9x + 1So,f(x+h) = (x+h)3 -…

Q: find the derivative by the limit process. f(x)=14-x^2

A: Here we find the derivative by the limit process fx=14-x2

Q: Find all points on the graph of the function f(x) = 2sin(x) + sin²(x) at which the tangent line is…

A: To find the points at which tangent line is horizontal, we must find slope of horizontal line. The…

Q: Suppose that the second derivative of the function y = ƒ(x) is y'' = x2(x - 2)3(x + 3). For what…

A: Given that, y=f(x) Second Derivative is y'' = x2(x - 2)3(x + 3). As we know that, Inflection point…

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) &gt; 0  from graph  Function is increasing…

Q: Consider the function f(x) whose second derivative is f''(x)=8x+8sin(x). If f(0)=4 and f'(0)=4, what…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: