Q5: Does any tangent to the curve y vx cross the x-axis at x--1 If so, find an equation for the line and the point of tangency? If not, why not?

Q: 18. Find the denvative or the runction y = 2x - 13x + 5 and use it to find an equation of the line…

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Q: For what value of x does the tangent line to the curve y=7+3e^x−6x  is parallel to the line 8x−8y=9?

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Q: f(x)

A: We will find the equation of tangent.

Q: 4. Find the point on the curve y = 2x² – 12x + 5 where the tangent is horizontal.

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Q: Does any tangent line to the curve y = 2x cross the x-axis at x = -1? If so, find an equation for…

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Q: 4 Find all the points on the curve x2 + xy + y? = 3 where the tangent to the curve is a vertical…

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Q: Find the slope of the tangent line to the curve V4r + y+ VIY = /13 + V10 at the point (2, 5). The…

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Q: 1. Find the slope of the given curve at the indicated point. y= x* – 3x? + 3 at (1,1) 2. Find the…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the slope of the tangent to the curve a+ 4xy+ y = 46 at (1,5). The slope is | (Enter undef if…

A: Topic = Derivative

Q: Q3: Find an equation for the tangent line to the curve y = etan x at the point where x = 0

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Q: Q1)a) Find line that are tangent the curve x2 + xy – y² = 1 at the point (2,3)

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

Q: 3. Find the equation of the tangent to the curve y = (x - 2)√x² + 16 at X = 3.

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Q: The equation for the tangent line to the curve y=x3 which passes through the point (0,2) is y=mx+b…

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Q: Q3: Find an equation for the tangent line to the curve y = etan x at the point where x = 0 (5 marks…

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Q: Q3/ Line A with equation y = -8x – 18 is tangent to the curve with the equation y = 4x + 2x? Find…

A: Given : The equation of the tangent line is y = -8x-18. The given curve is y = 4x+2x2

Q: A line is tangent to y = x - 2 at (2,6). What is the coefficient of x when the line is in the form…

A: Given curve y=x3-2    ;   (2,6)

Q: Find the equation of the line tangent to the graph of f(x)=4cos(x) at x=−π/3 Give your answer in…

A: Given :f(x) = 4cosx at x = -π3We will find the equation of tangent line

Q: 2) Find the points on the curve where the tangent is horizontal or vertical. x = t2 – 8t, y = 2t3 +…

A: A parametric equation of a curve is given by: x = t2 - 8t    and    y = 2t3 + 3t2  We have to find…

Q: At which points on the curve y = 1 + 60x3 - 2x5 does the tangent line have the largest slope? 1 5…

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Q: Find an equation of the form y = f(x) for a curve with r-intercept 2 whose tangent line at any point…

A: Here, to find the equation of the curve of the form y=f(x) with x-intercept 2. That is curve passes…

Q: Q3. Find the equation of the tangent line of the curve y= sinz + cos z at the point A(-, V2).

A: The given curve is y=sin x+cos x and at the point is Aπ4, 2  To find the equation of the tangent the…

Q: Find the equation of the tangent line to the curve y=4+e2sinx at the point (0,5).

A: our objective is to find the tangent line equation.

Q: At which point on the curve y = -2 + 2et – 3x is the tangent line parallel to the line 3x – y = 5?…

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Q: What is the slope of the tangent line that touches the graph of In y + e2z-1 = 3y – 4x at the point…

A: Given that: lny+e2x-1=y-4x

Q: 3. Find the equation of the tangent to the curve 3xy-y²= 7 at the point (.1).

A: Follow the procedure given below.

Q: At what point on the parabola y =  3 x2+ 2x is the tangent line parallel to the line y = 10x −2? Use…

A: First prinicipal : dydx=limh→0f(x+h)-f(x)h

Q: Find the point (x,y), at which the graph of y = 8x+6x-3 has a horizontal tanger The function y= 8x…

A: Our Aim is to find the point (x,y) at which the graph of y=8x2+6x-3-(i)has a horizontal tangent.

Q: (2) At what point(s) will the tangent line to y = x? - 4x +3 be horizontal

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Q: The tangent line to the curve ³ + y³ = 9xy at the point (4,2) intersects the y-axis at y = -1. -2.…

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Q: 2. Find the coordinates of the points on the curve y = r' - x² – x +1 where the tangent line is…

A: Solution:- step-by-step solution of above  question is given below.. The given curve is  y=x3-x2-x+1…

Q: Q4\ Find the slope of the function F(x) = √√x+1 at the point (8,3) And find the equation of the…

A: To find the slope of the function at the given point and also the equation of the tangent line at…

Q: Find an equation of the curve y = f(x) if y^n = 6x and the tangent line to the curve at (1, 2) is…

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Q: Find an equation for the horizontal tangent to the curve at Q. y = 1+ v2cscx + cotx

A: To find tangent line , find out the slope of the tangent line Take derivative to find out the slope…

Q: Q5: Does any tangent to the curve y = vx cross the x-axis at x=-1 If so, find an equation for the…

A: To find: The equation of tangent to the curve y=x if possible. Given: The equation of the curve y=x.…

Q: An equation of the tangent line to the curve y= cos(x) at a = T/3 is (- 7/3). %3D y =

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Q: 2. At which points on the curve y = 1+ 60x – 2x does the tangent line have the largest slope?

A: Solution ) y = 1+60x3- 2x5 First derivative with respect to  x y' =0+ 60 ×3 × x2 - 2×5 x4 y' = 180x2…

Q: Q#1. Find the x-coordinate of the point on the graph of y =x² where the tangent line is parallel to…

A: The given curve is  y = x2 Secant line cuts the curve at x = - 1 and x = 2

Q: 33. At what point(s) the tangent line have slope ? on the curve x = 3t² + 1, y = t³ – 1 does

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Q: At what point is the tangent line to the curve y° = 6x² perpendicular to the line 2x – y – 1 = 0?…

A: Given: y3=6x2..(1)2x-y-1=0y=2x-1...2   As we know that, iI two lines are perpendicular to each other…

Q: Q3)B/ Find the slope of the tangent line to the graph of x² cos(y) = 2y- eš* at the point (1? %3D 00…

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Q: Find the equation of the line tangent to the graph of f(x) = −3cos(x) at x = −π/3   Give your…

A: First, find the point of tang-ency. We know the x value we now have to find y value  Substitute in…

Q: Find the equation of the tangent line to the curve y= x4 + 6ex at the point (0,6). Enter exact…

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Q: Q4:a) find the equation of the tangent and normal line to the curve y = 10 - at point (6,4). ? 7-x…

A: (a) Given curve y2=10-67-x  The equation of tangent to the curve at point x1, y1, y-y1=dydxx1,y1x-x1…

Q: 6. Find the equation of the tangent line to the curve y = e when it is parallel to 2x- y=7.

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Q: At what point on the curve x = 9t2 + 6, y = t3 − 9 does the tangent line have slope 1/2?

A: Given parameteric equations of curve,   .x = 9t2 + 6 , y = t3 – 9   To find the point on curve…

Q: Find the equation of tangent line to curve x= t^(2)-2t and y=t^(2)+2t at the point t=2?

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Q: Find the equation of the line tangent to the graph of f(x)=−3cos(x) at x=−π/4 Give your answer in…

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Q: B) Find the slope of the line tangent to the curve y = sin3x at the point where x =

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Q: Q3) Find the equation of tangent line to the curve y/sin(x) +y²=2 at the point (,1).

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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: