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

6062 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Prove the identity: (sinx - tanx)(cosx - cotx) = (sinx - 1)(cosx - 1)


Prove, using the product rule that, the derivative of x^{n} is nx^{n-1} where n is a natural number. What if n is an integer or n is rational?


A medical test will be positive for 0.05% of people and negative for everyone else. Suppose a hospital will test 4000 patients each day. Use an appropriate approximation to find the probability that 5 people test positive tomorrow. (5SF)


How do i solve differential equations?


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences