The point A lies on the curve with equation y=x^0.5. The tangent to this curve at A is parallel to the line 3y-2x=1 . Find an equation of this tangent at A. [5 marks]

Differentiate equation

dy/dx=0.5*x-0.5

Gradient is the same as the second equation

2/3=0..5*x-0.5 

Solving this will give the x coordinate

x = 9/16 

Sub into equation for y coordinate

y = (9/16)0.5

Solve for C - constant (Y = Mx + C)

c = 3/4 - (2/3)*(9/16)

c = 3/8

Form equation

y = (2/3)x + 3/8

AM
Answered by Arnold M. Maths tutor

6157 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Sketch the function (x^4 + 2x^3 - x -2)/(x+2)


Given that y=x/(2x+5) find dy/dx.


2 equations intersect each other, y = x + 2 and y = x^2. Find the area of the shaded region between the points of intersection giving your answer to 3 significant figures. (shaded region will be shown)


A circle with centre C has equation: x^2 + y^2 + 20x - 14 y + 49 = 0. Express the circle in the form (x-a)^2 +(y-b)^2=r^2. Show that the circle touches the y-axis and crosses the x-axis in two distinct points.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning