Assume every secant line of the curve y = f(x) has slope at least 3. Then every tangent line of the curve y = f(x) also has slope at least 3.

Q: Find the slope of the tangent line to the graph of y = √x − 1 at the point (5,2).

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Q: Find an equation of the tangent line to the curve y = x - 3x + 5x that has the least slope.

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Q: Find the condition that the line ax+by=1 may be normal to the curve an-1y=xn

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Q: Show that the point (2, 4) lies on the curve x3 + y3 - 9xy = 0. Then find the tangent line and…

A: Given: f(x, y) = x3 + y3 - 9xy = 0 To find:  Equation of tangent and normal to the curve at point…

Q: Find the slope of the tangent line to the curve - 3æ² ³ = - 199 3x? + lœy+ 3y at the point (1, – 4).

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Q: Find an equation of the tangent line to the curve x2y² – 2x = 9-y at the point (-2, 1)

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Q: At what point on the curve x 3t2 + 1, y = t3 - 5 does the tangent line have slope ? (х, у) -

A: We have given curve as x=3t2+1         ⋯⋯1y=t3-5           ⋯⋯2 From the equation (1) and (2), on…

Q: Find the slope of the tangent line to the curve g²y -y = 6 at the point (1, 3). -18/5 0. -3 18 -5/18

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Q: Find the slope of the tangent line to the curve (a lemniscate) 2(x² + y²)° = 25(a² – y²) at the…

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Q: Let y(x) = . Estimate the slope of the tangent line of y(x) at the point æ = 0 : a+2

A: Solution

Q: Find the slope of the tangent line to the curve - 3x + lay+ 3y = 199 | %3D | at the point (1, – 4).

A: We are given a curve and we need to find out the slope to the tangent line at the point (1,-4). For…

Q: The slope of the line tangent to the graph of y = In(x²) at x = e² is %3D

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

A: we have to find an equation of the form y=f(x) for a curve with x-intercept 2 whose tangent line at…

Q: -1 Where on the curve y = (256+ x²)¯* does the tangent line have the greatest slope? NOTE: Enter the…

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Q: The slope of the tangent line to the curve y=2eUXcos(-6x) at x-0 is

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Q: Find the condition that the line ax+by =1 may be normal to the curve an-1y =xn

A: Given thatan-1y =xn Solution is as follows

Q: At what point on the curve x = 3t2 + 2, y = t3 – 2 does the tangent line have slope ? (х, у)

A: Slope of the line = dy/dx To get dy/dx, first get dx/dt then get dy/dt. Now divide dy/dt by dx/dt.5

Q: Write the equation of the tangent line to the curve (a lemniscate) 2(x2 + y²)“ = 25(x² – y²) at the…

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Q: Find the slope of the tangent line to the graph at the given point.

A: Slope:  The slope of a line measures the steepness of the line. The slope is calculated by rise over…

Q: Verify that (4,1) on the curve x + /xy = 6 and find the lines that are tangent and normal to the…

A: Given that, the curve is x+xy=6. Differentiate the curve x+xy=6 with respect to x as follows,…

Q: find the slope of the tangent line to the curve X2-4X3y2=-2 at the point (1,1)

A: The given curve is,

Q: Find the point (xo,yo) on the graph of y = x' + 9x² + 7x – 5, at which the slope of the tangent line…

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Q: at what point is the tangent line y3=2x2 perpendicular to the line x-y-1=0? P=(?,?)

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Q: Find the point (xo, Yo) on the graph of y = x³ + 3x² + 5x – 3, at which the slope of the tangent…

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Q: Show that the tangent lines to the curve y = (π sin x)/x at x = π and x = -π intersect at right…

A: The equation of the curve is y=πsinxx

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: Find the gradient of the tangent line to y when x =- 1

A: The explanation of answer as follows

Q: Show that the curve y = 2e* + 7x + 8x³ has no tangent line with slope 6. y' = y'[ ? ÷]6, so no…

A: We know that d/dx (x^n) =nx^(n-1) Please see the explanation below

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: Find an equation of the tangent line to the curve at the giv y = In(x2 - 3x + 1), (3, 0) y =

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Q: 3 at the point 7, 3 is: The slope of the tangent line to the curve y %3D

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Q: Find the point (x0, yo) on the graph of y = x + 9x² + 8x – 5, at which the slope of the tangent line…

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Q: Show that the tangents to the curve y2 = 4px from any point on the line x = -p are perpendicular.

A: The given curve is,

Q: Determine the values of x where a curve y=x³-3x²-9x+12 has horizontal tangent lines

A: Given,y=x3-3x2-9x+12differentiating both the sides w.r.t. xdydx=ddxx3-3x2-9x+12dydx=3x2-6x-9

Q: Find the slope of the tangent line to the graph at the given point. (x² + y²)² = 4x²y, (1, 1)

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Q: Find the points on the graph of y = ex where the tangent line has slope 4.

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Q: The Tangent Line to a y= f(x) at x = c has slope ?

A: Recall the below fact:

Q: Find the slope of the tangent line to the graph at the given point. (x² + y²)² = 4x²y, (1,1)

A: To find slope of tangent of a curve at a given point, we need to find differential at that point

Q: Find a curve in the xy-plane that passes through the origin and for which the tangent at (x, y) has…

A: Tangent is the line that just touches the curve at a single point. Derivative of the curve at a…

Q: Find the equation of the tangent and normal line using the stipulated conditions   1.) y = x2 - 5x…

A: Given the equation is y = x2 - 5x The point of intersection line y=6 The equation of the tangent is…

Q: Let y(x) = 2. x+2 Estimate the slope of the tangent line of y(x) at the point a = 0:

A: The given function is: y(x)=1x+2

Q: Compute for the interval [2, 7], where y = 3x - 3. Ay Ax Ду Дх What is the slope of the tangent line…

A: we have y= 3x-3at x=2y=3×2-3 =3at x=7y=3×7-3 =18so,∆y∆x = change in y over the intervalchange in x…

Q: Find the tangent line to the graph of x (x² +y² ) = y² at the point

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Q: slope of the tangent to the curve y2x+ y2x2 =6at (2,1) is

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Q: Show that the curve y = 6 x 3 + 5x -3            has no tangent line with slope 4.

A: y=6x3+5x-3 has no tangent line with slope 4

Q: find the slope of the tangent line to the graph at the given point. (x2 + y2)2 = 4x2y,   (1,1)

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Q: The slope of the tangent line to the graph of xy = In(x² + y²) at the point (1, 0) is

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: find the slope to the tangent line x^2e^4x at the point (-1,e^-4)

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