(c) Find the points on the curve xy? = 54 nearest the origin.

Q: (b) Investigate where the curve y = xy4 - x² is concave up and concave down?

A: Given curve is y=x4-x2 find the concavity of the given curve

Q: Find an equation for the tangent line to the parabola y = x² at the point P(1, 1).

A:

Q: Find an equation of the tangent line to the curve 2ax? +y² – 6x = 0 at the point P (1, -2)

A: Differentiate the equation with respect to x to find the value of dydx. 4x+2ydydx-6=0dydx=3-2xy

Q: Find the points on the curve xy2 = 54 nearest the origin.

A:

Q: Find the equation of y, glven the derlvative and the Indicated polnt on the curve. dy = 2x- 1 xp

A:

Q: ind the equation of the line tangent to the curve 3x² + 16y² = 192 at the point Mx + K. P= (-4, 3)…

A:

Q: Find the point in the first quadrant on the curve y = x + x - l closest to the origin.

A:

Q: Find the points on the curve x^2y = 2 nearest the origin.

A:

Q: 1. Consider the curve C given by y = 5 + 2x3/2, 0 < x <1. (a) Find the length of the curve C.

A:

Q: Find the exact length of the curve. x =Vy ( - 3), 1sys 25

A: given: x=13yy-3

Q: The x coordinate of the point of intersection between the two curves Y e14a and y = 1 is = x =

A: Given: y=e14xy=1

Q: Find the point on the curve y2 = ;(x+1) which is nearest the origin.

A: We have to find the point on the curve y2=52x+1 which is nearest the origin.

Q: Find the equation of the tangent line to the curve y? = xy + 6a? at the point (1, -2).

A: Given The curve y2 = x3y+6x2 and the point (1, -2)

Q: (d) Find the points on the curve x'y = 60 nearest the origin.

A:

Q: Find the points on the curve 5x + 5y? - 6xy - 6xy = 4 nearest to the origin.

A:

Q: Find the equation of the tangent to the curve x² +3y² = 6y at the point (1, ½)

A:

Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x 1+lnx b) y = -

A:

Q: 1) Given the curve 2x? + y3 = x3 + y? find the x-intercept of the tangent line at the point (2,1)

A: We find dy/dx using the implicit differentiation and we plug x=2 and y=1

Q: Find the values of a and b for the curve x2y + ay? = b if the point (1,1) is on its graph and the…

A: The slope of the tangent 'm' at a point (x1,y1) for a curve S(x,y) Is given by dydxx1,y1 therefore…

Q: b) Show that the equation of the tangent line to the x², y? Xox at (xo, Yo) is Yo.y + a² ellipse 31.…

A:

Q: Find the point on the curve y2 =;(x + 1) which is nearest the origin.

A: If (x, y) is any point on the curve nearest the origin then the square of its distance from the…

Q: Find the point on the curve y2 =(x+1) which is nearest the origin.

A:

Q: For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangent to the curve at x=2…

A:

Q: At the given point, find the line that is tangent to the curve. 5x3y - n cos y = 6t, tangent at (1,…

A: 5x2y-πcosy=6π=ddx(5x2y-πcosy)=ddx(6π)=10xy+5x2y'+πy'siny=0=(5x2+πsiny)y'=-10xy y'=-10xy5x2+πsiny…

Q: a)Find the exact length L of the curve 3y = (4x – 3), 1 0. Answer: b) Evaluate xe*dx Answer: .3 c)…

A:

Q: a. Determine the points where the curve 4x + 5y - y = 6 has a vertical tangent line. b. Does the…

A: a)  curve is 4x+5y2-y=6         Slope of tangent line is m=dydx    Differentiate the above equation…

Q: I Discuss the properties of the curve and sketch fully: a) y = x? e-x

A: (a) Given- y=x2e-x To Find- The properties of the curve and sketch the curve.

Q: 4. Consider the curve given by r³ + y³ = 9ry. Find the equation of the tangent line at (4,2).

A: To find the slope of the tangent we need dydx at (4,2)…

Q: Find the equations of the tangent lines x = t2 − t, y = t3 − 3t − 1 at the point where the curve…

A:

Q: Eliminate the parameter to find a cartesian equation of the curve x = t4, y = ln(t)

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: Find the exact length of the curve. y = 4 =Dx2-을 In(x), 1sxs6 =

A:

Q: ²+2x 5. Sketch the curve: y? x-1

A: The graph of the given function is plotted below.

Q: Find the slope of the parametric curve x = -2t3 + 1, y = 3t2, for - ∞ &lt; t &lt; ∞, at the point…

A:

Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x 1+lnx %3D

A:

Q: Find the equation of the tangent and length of the tangent to the curve y= x2+1 at (1,2)

A:

Q: 9. Find the point on the curve y x² closest to the point (0, 1).

A: As per bartleby guidelines we only give first question answers.

Q: B - Find the point on the curve y = x3 + x2- 1 where the tangent parallel to the x- axis.

A: Topic- slope of tangent and application of derivatives

Q: Find an equation of the tangent line to the parabola y=x2  at the point P(1,1)

A: To find an equation of the tangent line to the parabola y=x2 at the point P1,1

Q: The equation for the tangent to the curve y = t+ at the point (1,3

A:

Q: For what value or values of the constant k will the curve y = x3 + kx2 + 3x - 4 have exactly one…

A: Given curve is y=x3+kx2+3x-4. A curve have exactly one horizontal tangent  at x=a if f'a=0.…

Q: 2. Consider the curve given by 3y2 – 2x²y³ +2x +9 = 0. Write an equation for the tangent line to…

A: The given curve is, 3y2-2x2y3+2x+9=0 The slope of the tangent curve is given by dydx Determine the…

Q: Find the angles at which the curve y=x3−x intersects the x-axis.

A: The angle at which curve intersect the x axis is determined by the angle of slope of tangent to the…

Q: a. Determine the points where the curve 4x + 2y -y =1 has a vertical tangent line. b. Does the curve…

A: Consider the given curve 4x + 2y2 – y = 1

Q: a) y = x? e-X

A: We have to discuss properties of the graph

Q: For the curve y= ax + bx? + 12x - 7, what values of a and b will make the tangents to the curve at…

A:

Q: Find the points on the curve x2y = 2 nearest the origin.

A: The curve is x2y=2 Let x1,y1 and x2,y2 be two points, distance betwwen these points is x2-x12+y2-y12

Q: 1 Find the stationary points and state the nature of the curve y=xe.

A:

Q: Consider y = x2+3 /3e4x^2. Find the value of x at which this curve has a stationary point

A: Consider the given function.