Graph the function f(x)= x+4/x in the viewing rectangle [0, 10]× [0, 10]. Graph the secant line that passes through the points (1, 5) and (8, 8.5) on the same screen. Find the number c that satisfies the conclusion of the MVT on this interval. Graph the tangent line at the point (c, f (c)). Observe that it is parallel to the secant line.

Q: Find the equation of the tangent line to the function f(x) = x3 + a2 – x – 3 at the point where x…

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Q: Find all points on the graph of f(x) = x +a where the tangent line is parallel to the line y = 28x.…

A: Consider the function f(x) = x3 + x Slope of the tangent to f(x) is the derivative of f(x). f'(x) =…

Q: 3. For f(x) = /2x compute the slopes of the secant lines from 16 to each of 16± 0.01, 16 +0.001, 16…

A: When x = 16, f(x) = f(16) = √(2 x 16) = 4√2 =  5.6569  hence, slope of the secant line from (16,…

Q: Estimate the slope of the tangent line to f(x) = x³ at x=2 by finding the slope of the secant line…

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Q: Find the equation of the tangent line to the graph of f(x) at the given point. f(x) = V12x + 4 at…

A: The function is fx=12x+4 and the point is given as 1,4. Differentiate the function with respect to…

Q: Find the tangent line to the function f (x) = x² – 4x + 5 at the point (3,2).

A: To find: The tangent line to function fx=x2-4x+5 at the point 3,2. Formula used: The slope of…

Q: For the function ​f(x)=-3x^2 make a table of slopes of secant lines and make a conjecture about the…

A: It is known that the slope of a secant line between points (a, f(a)) and (b, f(b)) is given by:

Q: Find the equation of the tangent and normal line of the function f(x) = V2x – 1 at the point (5, 3).

A: fx = 2x-1     , 5,3f'x = ddx2x-1     = ddx2x-112        = 122x-1ddx2x-1        = 222x-1 = 12x-1∴f'5…

Q: Find all the value(s) of x at which f(x)=(7x^3/3)+3x^2−x+9 has a horizontal tangent line.

A: The values of x at which the given function has a horizontal tangent line can be found by evaluating…

Q: Find an equation of the tangent line at x = 3, assuming that f (3) = 5 and         f ,(3) = 2.

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Q: find the point (x,y) at which the graph of y=7x2+5x-6 has a horizontal tangent line.  The function…

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Q: Find an equation of the tangent plane to the graph of f(x, y) = 4x² – 7xy2 at the point (7, 8) z =

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Q: Find an equation of the tangent plane to the graph of f(x, y) = In(4x² – 2y2) at the point (1, 1). z…

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Q: Find the equation of the tangent line to the graph of the function f (x) = (x² + 8) (x – 3) at the…

A: The gradient of the tangent at any particular point is given by :     f(x) = (x2 + 8) (x - 3)…

Q: Find an equation of the tangent line to f(x) = 3x +5 at the point (1, 8).

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Q: Find an equation of the tangent line to f (x) = x² Vx4 – 12 at x = 2. - %3D

A: Explained below

Q: Find the slope and equation of the tangent line to f(z) = 5- 2z at a = 2 using the definition.

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Q: find a point c satisfying the conclusion of the MVT for the given function and interval. Then draw…

A: Given: y= ex  The average slope of y = f(x) = ex on [0,1] (f(1) - f(0))/1-0 e1 - e0 =  e - 1 = 1.718…

Q: Find the equation of the tangent line to the graph of the function f(x)=(x2+7)(x−2)fx=x2+7x−2 at the…

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Q: FIND THE SOPE OF THE TANGENT LINE TO 5x) AT THE POINT (x, 9(x)). 2.

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Q: Find the tangent line to the function y = x^2 at (1,1).

A: The given function is: y=x2 Now differentiate it with respect to x: y'=ddxx2y'=2x Put x=1 in y' to…

Q: Find the slope of the tangent line of the function -ey + x2 – y = 15 at the point (4,0)

A: Please note that the slope of tangent to a curve at any point is given by the derivative of the…

Q: Find a function f such that f'(x) = x“ and the line 2a - y = 3 is tangent to the graph of f. り

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Q: Find the equation of the tangent line to the function f(x)=x2−x+2 at the point where x=−1

A: The given function is fx=x2-x+2 and the x-intercept of a point is x=-1. Evaluate the corresponding y…

Q: Find a function f such that f'(x) = 2x' and the line 54x + y = 0 is tangent to the graph of f. (x) =

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Q: Find the equation of the tangent line to the graph of the function f(x) = v2x² + 1 at the point…

A: Given that: f(x)=2x2+1        at point (2, 3)

Q: Find the tangent line of the function f(x) = - 4Vx at x = 4, and the point at which tangent %3D line…

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Q: Let f(x) = (x - 12) / (2x + 6) Find an equation for the tangent line to the graph of f at x = 2 y =…

A: We find f'(x) first using quotient rule

Q: Find an equation of the tangent plane to the graph of f(x, y) = In(4x² – 2y2) at the point (1, 1).

A: To Determine: FInd the equation of tangent plane to the graph of…

Q: Determine the value(s) of x for which f(x)=9x+8 has a horizontal tangent line.

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Q: Find an equation of the tangent plane to the graph of f(x, y) = 4x² - 7xy² at the point (7, 8). z =

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Q: find a point c satisfying the conclusion of the MVT for the given function and interval. Then draw…

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Q: Find a function f such that f'(x) = r and the line 4r - y = 3 is tangent to the graph of f.

A: Given: f'(x)=x3Tangent line to the given curve is:  4x-12y=3Therefore: y=8x-6

Q: Suppose f (x) = (x 2 − 2x) (3x + 2).What is the equation of the line normal to f(i.e., the line…

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

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Q: Find the slope of the tangent line to the graph of the function at the point (1, 0). y 4 3 2 1 /1,0)…

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Q: Determine the value(s) of x for which f(x) = 9x + 8 has a horizontal tangent line

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Q: दलालभ यला Find an equafion of the tangent line to the ceurve at the grven point. y=x3-3x + 1, (2,3)

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

A: Given : fx = -3x3 -2x2 -1

Q: Find the equation of the tangent line to the graph of the function f(x) =x² - Vx at the point (1,0).…

A: We know tangent is a line and the equation of a line is given by y-y0 = m(x-x0)

Q: Find an equation of the tangent line to the graph of the function 2 x 4 2x+4 at the point (4, O Oy=…

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Q: Find the equation of the tangent line to the function f(x)=−4x2−3x+2 at the point where x=−1. Give…

A: we have to find tangent line to f(x) at x=-1given

Q: Find a formula for the tangent line to f(x) = x² – x at x = 0

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Q: Find an equation of the tangent line to the graph of the function f(x) = 4x – 2x3 at x = -1. Select…

A: Given: fx=4x-2x3   at x=-1

Q: Find the equation of the tangent line to the function f(x)=−3x3−2x2−1 at the point where x=−1. Give…

A: we have to find tangent line to f(x) at x=-1

Q: Find the slope of the tangent line to f(x) = x² – 3x at (-1,4). O 4 O -1 O 2x-3 O-5

A: Given query is to find the slope of the tangent at (-1,4).

Q: Find the equation of the tangent line to the graph of the function f(x)=(x2+8)(x−3) at the point…

A: Given: y=fx=x2+8x-3 at 0,-24 we know that for finding equation of tangent we need to find slopem of…

Q: Find the equation of the tangent line to the curvef (x) = 2x³ 3. - x at x = 2. o T(x) = 14 – 23(x –…

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Q: Find the equation of the tangent line to the function f(x) -x2 – 4x + 4 at the point where x = -2. =…

A: Answer is- Option 3 is correct Explanation is given below...

Q: Find the equation of the tangent line to the curve f(x)=5-x² at x = 2. O x-4y-2=0 O 4x + y +7=0 O 4x…

A: Find the equation of the tangent line to the curve f(x) =5-x^2 at x=2.