Find the equation of the tangent to the curve y=3x^2-7x+5 at the point (2, 3) .

The starting point for a question like this is to differentiate the function - in this case the curve y=3x2 -7x+5 . We calculate that dy/dx=6x-7 . The question tells us that we are interested in the case where x=2 . When x=2, dy/dx = 6(2)-7 = 5 . We want to find the equation of the tangent in the form y=mx+c . We can substitute in the information we already have (known point from the question and the gradient which we have just calculated) . This gives 3=5(2)+c . Re-arranging this equation gives c=-7 . And so we can finish this solution with the statement "the equation of the tangent is y=5x-7".

MS
Answered by Matthew S. Maths tutor

6984 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

C4 June 2014 Q4: Water is flowing into a vase. When the depth of water is h cm, the volume of water V cm^3 is given by V=4πh(h+4). Water flows into the vase at a constant rate of 80π cm^3/s. Find the rate of change of the depth of water in cm/s, when h=6.


What are radians and what are they used for?


Differentiate y = ln (3x + 2)


∫(3x+4)2dx


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences