15-18 A function y =f (x) and an x-value x, are given. (a) Find a formula for the slope of the tangent line to the graph of f at a general point x =x,. (b) Use the formula obtained in part (a) to find the slope of the tangent line for the given value of x,. 15. f (x)=x² - 1 ; x, =-1

Q: Let f(x) = 1/(x-5). Find the derivative f' of f. Find an equation of the tangent line to the curve…

A: This questions is related to differentiation,  We will solve it using given information.

Q: 1 Then find all x-values (if any) where the tangent line is horizontal. If the Use the definition of…

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Q: Assume that functions f and g are differentiable with f(2) = - 3, f'(2) = 4, g(2) = - 4, and g'(2) =…

A: givenf(2)=-3,   f'(2)=4g(2)=-4,   g'(2)=-3to find equation of tangent line on the following…

Q: The graph of the function f(x) = x/(1+x2) is called a serpentine. Find an equation of the tangent…

A: The equation of the tangent is, 3x + 25y = 16    The detailed solution is as follows below:

Q: 31-34 - Equation of a Tangent Line Find an equation of the line tangent to the graph of f at the…

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Q: For f(x) = x², the instantaneous rate of change is known to be - 6 at x = - 3. Find the equation of…

A: Given  that the slope of the tangent line of the curve fx=x2 and x = -3 is -6

Q: 3. What is the derivative of y = (f(g(f(g(x))))? Furthermore, if you are asked to evaluate the…

A: The given function,     y=fgfgxg0=0, f0=1 and g1=f1=1

Q: (a) find an equation of the tangent line to the graph of the function at the given point, (b) use a…

A: To find the equation of tangent, first find the slope by differentiating the function f(x)=12xlnx2…

Q: Assume that functions f and g are differentiable with f(-5)% = -4, f'(-5) = -4, g(-5)= -3, and…

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Q: a. Find the derivative of f at x. That is, find f'(x). b. Find the slope of the tangent line to the…

A: Slope of tangent is given by placing the given point in the first derivative of f(x).

Q: -가 Question-2 a) Find the derivative of f(x) = 2x? –- at x = 3 using definition of derivative at a…

A: As per our guideline we are supposed to be answer only one question

Q: The process of finding the derivative of a given function is equivalent to a. determining the…

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Q: 3-10 - Slope of a Tangent Line Find the slope of the tangent line to the graph of f at the given…

A: fx=3x+4 at 1,7slope=ddxfx=ddx3x+4                     =3Slope of the tangent line to fx at the…

Q: For f(x) = x, the instantaneous rate of change is known to be - 6 at x= - 3. Find the equation of…

A: Given  The equation is f(x) = x2 . The instantaneous rate of change is -6  at x=-3

Q: 8. Question: If you know the point (5, –1) lies on the function and that the point (2,7) lies on the…

A: Answer

Q: Assume that functions f and g are differentiable with f(- 3) = 4, f'(- 3) = - 4, g(- 3) = - 4, and…

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Q: An open box is to be made out of a 12-inch by 16-inch piece of cardboard by cutting out squares of…

A: We find V(x) in step 2

Q: 2 1 For f(x) = 2 + x2 the slope of the graph of y = f(x) is known to be 9 at the point with…

A: We have to find

Q: a. Find the slope of the tangent line to the graph of f at the given point. b. Find the…

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Q: For f(x) = x, the instantaneous rate of change is known to be - 6 at x = - 3. Find the equation of…

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Q: a).Find x value where the graph has a horizontal tangent line. f(x) = x^3 + x Using the fact that…

A: The given function is  f(x) = x3 + x Differentiate with respect to x , we get f'(x) = 3x2 + 1

Q: Question 13: Please refer to image attached. Thank you!

A: a) Average rate of change is given by (Population in 2018-Population in 2000)/18 =(f(18)-f(0))/18…

Q: 10/11 Find an equation of the curve whose tangent line has a slope of f'(x) = 3x given that the…

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Q: 6. (10 points) Give the equation of the tangent line of the following function at point a = 1: xe…

A: Solve by Differentiation

Q: II. Find the standard equation (slope-intercept form) of the tangent line to the given function at…

A: topic- equation of tangent line

Q: 3. Analyze using the tools of Calculus and sketch the graph of x³-1 f(x) = Otherwise write “none."…

A: Given function is fx=x3-1x3+1y=x3-1x3+1 a) To find the x-intercept substitute y=0…

Q: 1. the derivative of a function f is given by the formula x2 – 2x - 3 df (x) dx x - 1 (a). There is…

A: The expression, f(x)g(x) is undefined, if g(x)=0 . For the expression, f(x)g(x) , if g(x)≠0, and…

Q: 6) a) State the definition of f'(x), the derivative of a function f at value x. b) Use the…

A: We have to solve

Q: A function F(x) has a given value F(0) = -3. A graph of the derivative F'(x) is given below. What is…

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Q: 21-31 Find the derivative of the function using the definition of derivative. State the domain of…

A: The domain of the function f is, dom(f) = R, which is the set of all real numbers. And, the domain…

Q: 12) The concavity of a function is described by its? a) expressions b) first derivative c) second…

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Q: For f(x) = x², the instantaneous rate of change is known to be - 6 at x = -3. Find the equation of…

A: This question is based on finding equation of tangent line.

Q: Find the equation of the tangent line to the graph of the function f(x) = (z² + 6) (z − 2) at the…

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Q: a. Find the slope of the tangent line to the graph of f at the given point. b. Find the…

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Q: 21-31 Find the derivative of the function using the definition of derivative. State the domain of…

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Q: 18+x Find the absolute extrema of the function f(x) = on the interval [6,9]. %3D 18-x Find the…

A: See the attachment

Q: 16. The first derivative of the function f is given by f'(x) = 3x* – 12x'. What are the…

A: Given: first derivative of a function as f'(x)=3x4-12x3To identify the points of inflection of…

Q: a. Find the slope of the tangent line to the graph of f at the given point. b. Find the…

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

Q: a. Find the derivative function f' for the function f. b. Determine an equation of the line tangent…

A: The given function is  f(x) = 64x+1

Q: 2. If a function f(x) is differentiable at x-a, then function f(x) is continuous at? А. х-а В. х-х…

A: Given problems:-

Q: f(x) = √x; x = 1, x = 4. Solve, a. Find the derivative of f at x. That is, find f′(x). b. Find the…

A: fx=x⇒fx=x12 a. Differentiating with respect to x, we get f'x=dx12dx=12·x12-1…

Q: (9 points) For the function whose graph is shown below, find the value(s) of x at which t derivative…

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Q: 8) The first derivative of the function f (x) is given by its graph. [ A: 3] f'(x) 3 -5 a) Determine…

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Q: - 14 / 15 9. Find an equation of the curve whose tangent line has a slope of f'(x) = 3x given that…

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Q: a. Find the slope of the tangent line to the graph of f at the given point. b. Find the…

A: Given, f(x)=23x at (3,6)

Q: 1. Using techniques in calculus, solve for the exact or true value of the derivative of the function…

A: Topic - derivative

Q: At what point on the graph y=x/(x^2+1) the tangent line is parallel to the x-axis. Find an equation…

A: The objective is to solve the above questions.

Q: 5. a) Identify f, f', and f' from the graph below. b) Sketch the graph of the derivative in the…

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Q: 75. Derivatives from tangent lines Suppose the line tangent to the graph of f at x = 2 is y = 4x + 1…

A: The line tangent to the graph of f at x=2 is y=4x+1.