Find the paths orthogonal to the family of curves: cy ^ 2 = xe ^ x

Q: what point is the tangent line to y=1+2e* - 3x parallel to 3x - y = 5 ?

A:

Q: Find the shaded area of diagram that shecked by curve y = x2 + 2x and the line y = -x.

A:

Q: Find the points on the curve y = x4- 6x2 + 4 where the tangent line is horizontal.

A: y=x4-6x2+4 Differentiating with respect to x, we get dydx=4x3-62x+0=4x3-12x Now the tangent line is…

Q: Find an equation of the line tangent to the graph of y = exat x = 0.

A:

Q: Use the Difference Quotient to evaluate the slope of the tangent line to the first parabola found in…

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

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

A:

Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 3  where the tangent line is horizontal.

A:

Q: The slope of the tangent line to the curve y=2x^3 at the point (-4,-128) is ____. The equation of…

A:

Q: On the curve y3Dx2 ,find a point at which the tangent is parallel to the chord joining (0,0) and…

A:

Q: Find the length of the arc of the curve 9y2 = 4x3 from the origin to the point (3,2v3).

A:

Q: Find length of arc of the curve 9y2=4x3 from the origin to the point (3, 2√3)

A: Given curve is 9y2=4x3, and the point is 3,23.   The objective is to determine the length of arc of…

Q: Write the equation of the tangent line to the curve y = x3 + 3x - 8 at (2, 6).

A: To find the equation of the tangent line to the curve y=x3+3x-8 at (2,6). Solution: We know, The…

Q: Find an equation of the tangent line to the curve y= x3 – 3x2 + 5x that has the least slope.

A: Given    slope is 1st derivative

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: the guidelines of this section to sketch the curve: y = x+ – 8x

A:

Q: Find the slope of the tangent line that passes through point (1, 2) to the graph 8y³ + x²y O-2/97…

A:

Q: Find an eqaution of the tangent line to the curve at the given point. y = 4x - 3x2, (2,-4)

A: The given function is y=4x-3x2 and the point is 2,-4

Q: Find an equation of the tangent line to the curve y 9tanx at the point %3D

A:

Q: Find the points where the line y=x4 intersects a circle of radius 2 centered at the origin. Give…

A:

Q: Describe the tangent line at an arbitrary point on the graph of y = 2x + 8

A: we have to describe the tangent line at an arbitrary point on the graph of y=2x+8

Q: Find the tangent and normal lines to the curve ペー9ーチ at the Pomt (-62)

A: Given, The equation of the curve  x2-xy+y2 = 7  We have to find the equation of tangent and normal…

Q: Find the exact length of the curve y3 = 22 from (-1,1) to (8, 4).

A: Use formula of length of curve

Q: Find an equation of the tangent line to the curve at thegiven point. y= 4x  - 3x2 ,    (2 ,-4)

A: we have to find an equation of the tangent line to the curve y=4x-3x2 at the point (2-4). as we know…

Q: Find the equation of the tangent line to the curve y = rVI at the point (4, 8). %3D

A: We have to find the equation of tangent

Q: what is the slope of the tangent line to the curve 8x^3 - y^2 = 4 at the point (1,-2)

A: Given,

Q: Find one point on the curve where the tangent line is horizontal y2=x3-3x

A: We have the equation of given curve as y2=x3-3x Now, the slope of the tangent can be calculated as…

Q: Find the equation of the tangent line of funclion y= ²+1 23 -2 at (40,- 73)

A:

Q: Find the slope of the tangent line to the parabola y = x2 at the point (2, 4) by analyzing the…

A: We have to find the slope of tangent line to the given parabola y=x2 at the point 2, 4 by analyzing…

Q: Give an equation for the tangent line to = 1 at the y2+1 point (5,2) and sketch it on the graph. -5-…

A:

Q: Find the orthogonal trajectories to the family of curves:

A: Consider the given equation. x2=C-12y2lny2-1 Find the derivative of the function with respect to x.…

Q: Find the points on the curve y = 2x3 + 3x2 – 12x + 1 where the tangent line is horizontal. (х, у)…

A: Solution ) given f(x) = y = 2x3 + 3x2 - 12x + 1 f'(x) = 2 × 3 × x3 - 1 + 3 × 2 × x2 - 1 - 12 + 0…

Q: The slope of the tangent line to the curve y = 3 3 at the point (5,2) is: X -

A:

Q: find the equation of a tangent line for y=arcsin(x/8) at the point (4,π/6)

A:

Q: Find the tangent line at (-1,3) to the curve y* – 2x*y' - 27=0.

A: Given, The equation of the curve    y4 -2x2y3 -27 = 0  We have to find the  tangent line at -1, 3 .…

Q: Determine the equation of the line tangent to the curve square root(xy)=x-2y  at point (4,1)

A:

Q: Find the slope of the tangent lines on the curve y = 6x^3 +24x^2 -39x -43 at poins (-5, 2) and (1/3,…

A: We know that, The slope of the tangent line to the curve at a given point Px1,y1 is equal to the…

Q: Find where the tangent line to y= (5x-1)2 (4x+7)3 is horizontel.

A:

Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 6  where the tangent line is horizontal.

A:

Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 2 where the tangent line is horizontal

A: To obtain the points where the tangent line is going to be horizontal to the curve, we need to find…

Q: Does this curve go through the point (-1, 1, -1)?

A:

Q: Show that the curve y =6x3 +5x -3 has no tangentline with slope 4.

A: Consider the following equation of curve: y=6x3+5x-3 Differentiate y with respect to x:…

Q: Show that the curve y = 2ex + 3x + 5x3 has no tangent line with slope 2.

A: To show that the slope of the tangent at every point is different form 2, for the given curve

Q: Find an equation of the tangent line to the curve at the given point. y = 2x2 - 8x + 1, (5, 11) y =…

A: To find: The equation of tangent to the curve y=2x2-8x+1 at 5,11. Given: The equation of curve is…

Q: Find the slope of the tangent line to the curve y 3x-8x + 7 at the point (-1,2). -3 3. -4 4

A:

Q: Find the point on the curve y = 3x + 4 which is closest to the point (5, 0). Preview Preview

A: Let (x, y) be the point closest to the point (5, 0) We will calculate the distance between these two…

Q: Find an equation of the tangent line to the graph of y = arcsin(2x) at the point 2/2 4

A:

Q: Find the differentual equatrion characterizing the family of curves described

A: Given that: ky=x2

Q: Find the tangent line at (-1,3) to the curve y* – 2x²y' – 27=0.

A:

Q: Determine the slope of the tangent line to the curve y=2 – x2 at the point (3,-7)

A: slope of tangent = slope of given curve  step 1  we have to find slope of curve  slope = dy/dx  so…

Q: Find the exact length of the curve over the given interval. 2sxs3 4x'

A: