22. For the following functions, identify any points of discontinuity, and if any exist, classify cach point of discotinuity as either removable or non-removable. [2x' +3 xs a) f(x)- x+4 b) gta) -

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: Verify Rolle's theorem for f(x) = x* – 4x+8 over the interval [0, 2].

A:

Q: Find the line tangent to the graph of f(x) = x² + x +1 at xo = 2

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Q: Find an equation for the line tangent to the graph of f at (2,15), where f is given by…

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Q: The slope of the tangent line to the graph of f(x) D x2 at a = -1 is: %3D %3D

A: Given  equation of the graph  f(x) = xx2-x                        ...........(1) We have to find the…

Q: 1. Given the graph of f', the derivative of f, locate all extrema of f. JUSTIFY. Minimum at x =…

A: To find the minima and maxima from the graph of f'(x)

Q: what is the largest vertical distance between the graphs of the functions y=x^1/2 and y=x^2 in the…

A: To find the largest vertical distance between the graphs in the interval given

Q: 4. Determine the point(s) at which the graph of f (x) = has a horizontal tangent. Simplify as much…

A:

Q: Find all value of x=c, so that the tangent line to the graph of f(x) at (c,f(c)) will be horizontal…

A:

Q: Suppose the linear approximation for a function f(x) at a = 2 is given by the tangent line y = −2x +…

A:

Q: Suppose f(3) = 6 and f '(3) = 7. Find an equation of the tangent line to H(x) at x=3. %3D H(x) =…

A: We have,  Hx=x4-7fx, f3=6 and f'3=7 Using the chain rule of differentiation, H'x=x4-7·f'x+fx·4x3…

Q: 9. What is the equation of the line tangent to the graph of the function f at the point (1,1)? f (x)…

A:

Q: 4. A. Use the tangent line to find a linear approximation to the function f (x) = Vx near x = 64.…

A:

Q: The tangent lines which was drawn at points A and B on the following y = f (x) function graph are…

A:

Q: 2. Determine the slope of the tangent for the following function: 3x f(x) at x = 4 2 x-4x+3

A:

Q: If f(x)=sqrt x, find the linearization L(x) at a=4. Thus the graph of L(x) would be tangent to f(x)…

A: Given information: fx=x ,  at a=4 Formula of Linearization  Lx=fa+f'ax-a

Q: ) Find the equation of the tangent line ETL for f(x) = x³ - 2x +1 at x = −1

A:

Q: For what values of x in [0,2pi] does the graph of f(x)= x + 2sin(x) have a horizontal tangent?

A: Horizontal tangent:The slope of a tangent of the graph of a function f (x) is df (x) ∕dx. For a…

Q: 57. Is the function given by Sx + 1, for x 4, g(x) = continuous at x = 4? Why or why not?

A: gx=12x+1,   for  x<4-x+7,   for  x>4 Now left hand limit at x=4 is, limx→4-fx=limx→4-12x+1…

Q: 2. Find the points on the graph of f(x) =- where the tangent line is horizontal. x2+2

A: Given f(x)=xx2+2we want to find the point on curve where tangent is horizontal

Q: The tangent line to y = f(x) at (0, –8) passes through the point (7, 4). Compute the following. a.)…

A: Given: y = f(x) at (0,-8) Passes Point ( 7,4)

Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

A: Topic- application of derivatives

Q: The equation of the tangent line to the graph of f(x) = vx+1 At the indicated point (3,2) is:…

A: The given function is fx=x+1. Evaluate the slope of the function at the point (3, 2) as follows.…

Q: Where is the function f(x) = if x 0 removable discontinuity? Is it a jump discontinuity?

A: A jump discontinuity occurs when right and left limit exists but are unequal .

Q: calculate the are between the curves f(x)=x^2 and g(x)=x^3 on the interval [-1,1]

A: Given,

Q: 6. The tangent to the function f(x) = ke2x at x = has slope 2e. Find the value of k.

A:

Q: The fifth-order partial derivative ∂5ƒ/∂x2∂y3 is zero for each of thefollowing functions. To show…

A: We have to find which variable should we choose so that we differentiate as quickely as possible.

Q: Find the equation of the tangent line to the graph of the function f (x) = 4xcosx + 3 at the point…

A: Given that: f(x)=4x.cosx+3 at point (0, 3)

Q: Find the equation of the line tangent to the graph of f(x)=−3cos(x) at x=−π3

A: As we know that: The first derivative of the function is equal to the slope of the tangent line to…

Q: 2) Find the point(s) at which the graph of f (x) = has a horizontal tangent. x2+1 %3D

A:

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

A:

Q: Is the function given by f(x) = 5X+6, for x s5, 5x-14, for x>5, continuous at x=5? Why or why not?

A:

Q: Find for the following function: 1- y = etan'x 2-x'y+ x*y 2 at x = 2

A:

Q: 2. Find the slope of the tangent line to f(x)=V4-V+5 at the point where x 4.

A:

Q: For what vaules of x in the interval [0,2π) does the fraph of g(x)= (√3)x+2sinx+7 have a horizontal…

A: For horizontal tangent,first derivative must be zero

Q: Let f(x) = 2x + 3 – 17e". Find the equation of the tangent line to the graph of f(x) at the point…

A:

Q: Find all x-values where f(x) = (x² + 2x – 3)4 has a horizontal tangent line.

A: We find f ' (x) using the chain rule and the power rule. f(x)=(x2+2x-3)4…

Q: The slope of the tangent line to the graph of the function y = 7 x – 3 at (9, 18) is. O -2.67 O 1.17…

A: We know that dy/dx gives slope of tangent at any point.

Q: The point on the graph of f(x) = 1 where the tangent line is parallel to the line 3z + y = 1 is: %3D

A:

Q: Find f(4) and f' (4), assuming that the tangent line to y = f(x) at a = 4 is y = -6x + 2. %3D

A:

Q: The tangent line to y=f(x) at (−5,−3) passes through the point (7,−3). Compute the following. a.)…

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Q: Find the absolute extrema for the function over the specified domain. y = x2 5 over [ – 1, 2] -

A:

Q: On what interval is the function f(x) = x^3 - 4x^2 + 5x concave upward?

A: Use given function find the required result

Q: The slope of the tangent line to the graph of the function y = 5/T – 4 at (16, 16) is , O -1.50 O…

A: We have to find the slope

Q: Find all points ( x,y) on the graph of f(x) = 3 x² – 4x with tangent lines parallel to the line y=…

A:

Q: Find points of discontunity of the function,where k is real number 1 f(x, y) sin(4 – x2 – y?) - -

A:

Q: 7)Determine the points at which the graph of the function has a horizontal tangent line. f(x) х3 %3D…

A:

Q: The slope of the tangent line to the graph of the function y = 8/T- 4 at (16, 28) is O 4 O -1.75 O…

A: Slope : It is the Differentiation of y with respect to x at a given point.

Q: 22. If the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f'(4).…

A: #22 f(4) ? f'(4)?

Q: Find all r-values where f(x) = (x2 + 2x - 3)4 has a horizontal tangent line.

A: The function f(x)=x2+2x-34. We have to find all x-values where the function f(x) has a horizontal…