At which points on the curve y = 1+40x3 – 3x does the tangent line have a locally maximum slope? A locally minimum slope? (Be sure to justify which is which.)

Q: [3] If the curve is defined by y = x* – 8x3 + 22x2-24x+9, then what are the value/s of x for which…

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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: 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: 4. At what point on the graph of y =x2 is the tangent line parallel to the line 2x – 4y = 3?

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Q: 5. Hance sits at one of the points on the curve y = 2x³ -3x²-12x +20 where the tangent is parallel…

A: Please see the below picture for detailed solution.

Q: Find the slope of the tangent line at the point P = (1, 1) on the graph of              ex-y = 2x2 -…

A: Given,          ex-y = 2x2- y2    at   P=(1, 1)

Q: 3. Find the slope m of the tangent lines to the parabola y = -x+ 5x+ 6t its point of intersection…

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Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 6x – 3, at which the slope of the tangent…

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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: Find an equation of the tangent line to the curve at the given point y = 4x2 – x, (1, 3)

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Q: Find an equation of the tangent line to the curve at thegiven point.   y= x3- 3x -1 , (2, 3)

A: The given equation of the curve is y= x3- 3x +1. We have to find the tangent line to the curve y=…

Q: Show that the curve y = 7e* + 3x + 2x³ has no tangent line with slope 2.

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

A: We have to find the point

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: Find the equation of the tangent line to the graph of y = -2x° + 6x? – 5x + 10 at the point (1,5) in…

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Q: Find the equation of the tangent line to the graph of y = 2x - (4 / √x) at the point (4, 6).

A: Given,            y = 2x - 4x and Point is 4, 6

Q: Find an equation of the tangent line to the graph of Y = e2x-3 at the point (3/2,1).

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Q: Show that the curve of y = 2e2z + 3r + 2r3 has no tangent line with slope 2.

A: The given curve is y=2e2x+3x+2x3. Obtain first derivative as follows. dydx=ddx2e2x+3x+2x3=4e2x+3+6x2

Q: Find the​ x-coordinates of all points on the curve y = (-x^2+4x−3)^3 with a horizontal tangent…

A: We know the slope of the tangent where it is horizontal is 0. we will need to find the derivative of…

Q: Therefore, the curve y = x* - 2x2 + 2 has horizontal tangents at x-0, 1, and -1

A: Just compute the derivative and equate it to zero.

Q: Find an equation of the tangent line to the curve at thegiven point.

A: Given: y=2x+1x+2, 1,1 for finding equation of tangent, we need to find slope of tangent  we know…

Q: Find the point (xo, yo) on the graph of y = x + 3x² + 4x – 5, at which the slope of the tangent line…

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Q: What is the slope of the tangent line to the graph of any quadratic function of the form y=ax²+bx+c…

A: First find the vertex of the parabola, y=ax2+bx+c . Then, compute the expression for dydx .…

Q: At what points on the curve x2 +4y2-12=0 are tangent lines vertical?

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Q: Show that no point on the graph of x 2 - 3xy + y 2 = 1 has a horizontal tangent line.

A: Given  x 2 - 3xy + y 2 = 1

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 the point (xo, yo) on the graph of y = x³ + 3x? + 8x – 3, at which the slope of the tangent…

A: To find the slope of the function we need y'y=x3+3x2+8x-3y'=3x2+6x+8

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 point (x0,y0) on the graph y=x^3 + 6x^2 +3x -5 at which the slope of the tangent line has…

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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: At what points on the given curve  x = 2t3, y = 4 + 16t − 10t2  does the tangent line have slope 1?

A: The tangent line of any given function is the line which  touches the curve of function at only one…

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

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Q: What is the slope of the tangent line that touches the graph of In(y)+e2x-=3y – 4x at the point (A 1…

A: The solution are next step

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: Find the point (xo, yo) on the graph of y = x + 9x2 + 3x - 4, at which the slope of the tangent line…

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Q: The curve y = [In (x + 4)]² has horizontal tangent line at the point(s)

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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: At which points on the curve y = 1+40x³ –3x does the tangent line have a locally naximum slope? A…

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Q: a) Find the slope of the tangent to the curve y = 3+ 4x2 – 2x³ at the point where x = a.

A: We are suppose to solve the problem by application of derivative.   NOTE :: As per our guidelines we…

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: a. Determine the points where the curve 5x + 3y - y= 5 has a vertical tangent line. b. Does the…

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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: 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: 4. At what points on the curve y = 2x³ – 3x2 – 2x + 4 are tangents of slope 10?

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

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Q: Find an equation of the tangent line to the curve at the given point. y = In(x² - 3xt 1), (3, 0) y…

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