Find the exact value of fo f(x) dz for the function f(x) graphed below.

Q: ) Find a function ƒ such that f'(x)= x³ +3 and such that the line y+5x O is tangent to the graph of…

A: Given, f'(x) = x3+3  and the line  y +5x =0 is tangent to the graph of f   Let's assume the function…

Q: Given the function g(x) = 2^x , along with the tangent line to the graph at x = 0, may you help me…

A: g(x)=2x  , Tangent line at x=0 Apply definition of derivative g'(x)=limh->0.01g(x+h)-g(x)hReplace…

Q: Find f'(x) and find the equation of the line tangent to the graph of f at x= 2. X-6 f(x) = 5x - 1

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Q: For what values of x does the graph of f(x)=2x^3+15x^2−36x−5 have a horizontal tangent line?

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Q: find the points of inflection and discuss theconcavity of the graph of the function. y=x-\ln x

A: Consider: y=x-ln x. Find the inflection points and concavity of function. First find the domain of…

Q: given the function f(x) = x² – 3x + 1. Use this function to find The equation of the tangent line to…

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Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 19 – x²;…

A: The given data is: gx=19-x2 To find the slope of the tangent line at the point 3,10.

Q: 1. For the function f(x) = 3x² + 7x – 2, (a). Find the slope of the tangent line at x = 4. (b). Find…

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Q: The function f is defined by f(x) = \25 – x² for -5 sx 5. (a) Find f'(x). (b) Write an equation for…

A: Given: fx=25-x2; x∈-5,5 we know that for finding derivative of given function, we differentiate…

Q: Find the domain of the function. f(x) = √(ln x)

A: To find domain of the function fx=lnx. Solution: Domain is the input value for which a function is…

Q: The derivative of the function f (x) = (x-1 – 2)(3 – Vx) is,

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Q: Determine the point(s) at which the graph of -8x f(x) 2x - 1 has a horizontal tangent. (x, y) = Need…

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Q: Let f(x) = x^2(ln x − 1) (e).Find the inflection point(s) of the graph of f, if any.

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Q: In the given question , find all functions f having the indicated property? The tangent to the graph…

A: Explanation: Given a function f(x) and point of tangency (x,y). Also given that, the tangent line…

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = Inx?;…

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

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Q: (b) Write the equation of the line tangent to the graph of f(x) at z 1, and graph it below f(x) =…

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Q: For the function f(x), defined graphically, state the value(s) of x where the function is not…

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Q: Find the function f given that the slope of the tangent line at any point (x, f(x)) is f'(x) and…

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Q: Use the graph of the function f to find approximations of the given values. y 4-

A: To find the values of f at x= a,  we imagine the vertical line x=a and where the vertical line…

Q: Find the derivative. f(x) = e. 3x

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Q: Find the anti-derivative of the function and evaluate. g(x)=2x g(0)=7

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Q: f(x) 5 1 -1

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Q: Let f(x) = 4x3 + + 2Vx – 7. Find f'(x). 15. Find an equation for the tangent line to the graph of…

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Q: Let f(x) = (x - 8)(2x +7). Find an equation for the tangent line to the graph of f = 7. at x =…

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Q: For what value(s) of x does the graph of f(x)=10x^3 − 90x^2 + 240x +90 have a horizontal tangent?…

A: To find the slope of the tangent we find f'(x)

Q: Q1) A) Find the tangent equation for the function: f(x) = Vx +5 at x-2? %3!

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Q: O For what value of x does the function f (x) = 4x2 – x +1 have a horizontal tangent?

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Q: Determine an equation for the line tangent to the graph of the given function at the indicated point…

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Q: 8. 4 2

A: In this question we will use basic of calculus i.e use of tangent function. We will write the…

Q: 5. y = xArctanx - In V1+x

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

A: Given,           fx=x2-x4 ; x=1To find : Find f'x and find the equation of the tangent line at the…

Q: Let f(x)= e^x^2 . Find an equation of the line tangent to the graph of f at the point the (1,e).

A: Tangent to the graph,

Q: Find f'(x) and find the equation of the line tangent to the graph of f at x = 1. f(x)= (1 +5x)(3-2x)…

A: topic- derivative and equation of tangent line to function

Q: Find the derivative. F'(x) if F(x) = (e×" + 1) °

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Q: 1. For the function f(x) = 3x² + 8x – 7, (a). Find the slope of the tangent line at x = 2. . (b).…

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Q: Find the derivative of the function. G(x) = V1- 9x2 · arccos(3x) G'(x) =

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Q: Find an equation for f(x) using the secant function. f(x) =

A: NOTE: Refresh your page if you can't see any equations. . the secant function is in the form of as…

Q: For what value(s) of x does the graph of f(x) = 8x³ – 84x² + 288x – 48 %3D have a horizontal…

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Q: 5. x= y= t2-1

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Q: Q4. Find the slope of the tangent line to the function f(x)= e* +3; x+2 at x=4 5x-10

A: Given : fx = ex5x-10

Q: What is the first derivative with respect to x of the function g(x) = 3/9 9. O 1/2

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Q: Find the following derivative 1 g(x) = 2* · (x² + 1)

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Q: Find the first derivative f' and the original function f. f"(x) = x³ – 48x, f'(1) = 0, f(1) = 16

A: We have to find f'(x) and f(x).

Q: Find the values of x where the tangent line is horizontal for the function  f(x) = x2(x-5)3

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Q: For the function f(z) = ¹, the point z 1-e Z = 0 is

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Q: Find the derivative f'(x) for the function f(x) = x² + x – 17. - O A. f'(x) = 2x – 16 В. f («) — 2а…

A: Find the derivative of f(x)

Q: Find the derivative or f'(x) for the following: dx y= x²- 3x + 4 2х-5 (x) = 3x+2

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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: