Compute the slope of the secant line containing the points (1, f (1)) and D) on the graph of f (x) = (x – 5)(x – 2)(x +1)(x + 4). Show the calculatie

Q: Find all points (x, y) on the graph of g(x) = x3/3 -3x2/2+1 tangent lines parallel to the line 8x -…

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Q: Find all points of the graph of f(x) = 3x2 + 9x whose tangent lines are parallel to the line y - 57x…

A: Solution: Two lines are parallel if they have same slope.

Q: 5. Find using first principles the slope of the tangent to f(x) = x² + 6x + 9 at x = -3.

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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 a point c satisfying the MVT for the given function and interval. 2 y = x3 [0,8]

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

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Q: Find the equation of the tangent line to the graph f(x) = 2x² + 5 at P(-1,7)

A: We will find out the required equation of tangent.

Q: Find all points (x, y) on the graph of f(x) = x - 3x + 8x + 23 with tangent lines parallel to the…

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Q: Find an equation of the secant line containing (1, f(1)) and (2, f(2)). f(x) = x² - 2x

A: Rule:-equation of line passing thraught (x1,y1) and (x2,y2) is y-y1=y2-y1x2-x1(x-x1)

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: The slope of a tangent to the curve f(x) = x² + 2x – 5 at the point (3, 10) is : 12 8. -5 10

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Q: Find all points (c, f(c)) on the graph of f(x) = x3 −3x2 where the tangent line has slope 9.

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Q: Find an equation of the tangent line to the graph of f (z) = -2² + 3z – 2 at the point (2, 0)

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Q: Find the points on the graph of f (x) = x3 − 3x2 + x + 4 where the tangent line has slope 10.

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Q: The slope of the curve f(x)= at x =1 is

A: given function :

Q: Find the orthogonal trajectories for the family of curves x2 − 2y2 = C . Use a graphing utility to…

A: Concept: Trigonometry is used in finding distance and angles, there are six trigonometric ratios…

Q: Determine the coefficients a, b, c and d so that the curve y = ax³ + bx² + cx + d be tangent to the…

A: Curve y=ax3+bx2+cx+d is tangent to the line y=3x+8 at the point (-2,3). The curve y=ax3+bx2+cx+d has…

Q: Find a formula for the linear function f(x) with slope 2 and vertical intercept 1. f(x) =

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Q: Find the point on the graph of y = 3x2 − 2x + 5 where the tangent line is perpendicular to the line…

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Q: Find all points (x, y) on the graph of f(x) = x° - 4x + 15x + 10 with tangent lines parallel to the…

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Q: 4) Find an equation of the line tangent to the graph of 2x³y³ = 2y – 4x at the point (-1, –1). Show…

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Q: Find an equation of the tangent to the curve f(x) = 2x2 - 2x + 1 that has slope 2.

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Q: 5. Find the equation of the line tangent to the graph of f(x)= 2x' +4x² – 5x– 3 at | x = -1.

A: f(x)=2x3+4x2-5x-3diff w.r.t xf'(x) =6x2+8x-5now substitue x=-1f'(-1)=6(-1)2+8(-1)-5f'(-1)=-7slope of…

Q: 4. Find the equation of a line tangent to f (x) = –x² – 4x at x = -1.

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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 equation of the tangent line to f(x)=−2x−4x^−1/2+3 at the point (4,−7).

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Q: f the line tangent to the graph of y =x* – 2x + 1 at x =-1

A: Idea: find the slope of tangent line by differentiation at x=-1 .then find the point on the curve.…

Q: Find all points (x, y) on the graph of f(x) = x° - 4x + 20x + 11 with tangent lines parallel to the…

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Q: Find the equation of the line tangent to the graph of f(x) = 4x° + 6x2 – 6x – 5 at x = -6. %3D

A: The function is given by fx = 4x3+6x2-6x-5 To evaluate: The equation of the tangent line to the…

Q: Determine the point(s) at which ƒ(x) = x3 - 12x has a horizontaltangent line

A: The points where the tangents are horizontal are the points at which slope is zero.That means,…

Q: 6. Determine the x-value(s) of the point(s) on the graph of f (x) = 3x³ – 11x – 2 where the tangent…

A: The function f(x)=3x3-11x-2 where the tangent line is parallel to the line 10x-2y-18=0

Q: 3. For f(x) = x -5x-6, make a table of slopes of secant lines and make a conjecture about the slope…

A: As we know that the slope of the tangent line is given by, dydxx=a=limh→0f(a+h)-f(a)h If a = 6, then…

Q: Consider the function f(x,y) - x-44x- 4y and determine if, at the point (4,0) if the function is a…

A: Note: Since you asked multiple questions I solved one. For solution of other problem please post the…

Q: find all points (x,y) on the graph of f(x)=3x^2-5x with tangent lines parallel to the line y=7x+1.

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Q: Find the critical points of y= -2x^2 +4x +3 and apply the Second Derivative Test to find the maximum…

A: Critical point and extreme points

Q: Show that the slope of the secant line for f(x) = x 3 - 2x over[5,x] is equal to x 2 + 5x + 23. Use…

A: Given: y=fx=x3-2x; 5,x we know that slopem of secant for any given functionfx over a,b is given by…

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: Find the equation of the tangent line to the graph of f(x) = x² – 4 at the point (3, 5). -

A: The equation of the line passing through the point (x1,y1) having slope m is given as (y-y1)…

Q: Compute the equation of the horizontal asymptote of the curve y = (2x- 1)/ (x + 2). y = 2 x = 2 X =…

A: Given; y=2x-1x+2   As we know that; To calculate the horizontal asymptote, solve the limit…

Q: find an equation of the tangent line to the graph of f(x)= 5x^2-7 that is parallel to the line…

A: The general equation of line in slope intercept form is y=mx+c where m is slope and c is…

Q: Find the values of x at which the graph of f (x) = 4x² – 3x + 2 has a tangent line parallel to the…

A: Note : As per our guidelines we are supposed to answer only one question. Kindly repost other…

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

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Q: Find the equation of the line tangent to the graph of f(x)= 7x³ +5z2 - 3z- 3 at z = -5. %3D

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Q: Find the equation of the line tangent to the graph of f(x) = 5x° +4x² – 5z – 6 at z = -6. %3D

A: Given that       f(x) = 5x3+4x2-5x-6      at x=-6 Here we have to find the equation of the line…

Q: 4. Jacobi is seated on the line tangent to the graph of  y =2x3 -3x2 -12x +21 at x =2.

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Q: The gradient of the tangent to the curve y=-3x³ + 4ax² - 5x + 4 at x = 1 is 2. The value of a is 2.…

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Q: Determine the co-ordinates of all the points at which the tangent to the curve y = 3x'e8x is…

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Q: Find the point where the tangent to the graph of f(x)= -x^2-6 is parallel to the line y=4x-1

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Q: Find all points (x, y) on the graph of y with tangent lines perpendicular to the line y = 4x - 5. (x…

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