Find the equation of the tangent to the curve y = 3x^2 + 4 at x = 2 in the form y = mx + c

There are two main steps. First find the gradient of the curve at x = 2 (m). This is done by differentiating the curve equation y = 3x^2 + 4 to get dy/dx = 6x. By plugging in x = 2, we get the gradient of the tangent, m, as 62 = 12. Then we need to find the y intercept of the tangent, c. We make c the subject, so c = y - mx. We worked out what m is (12) so we just need a set of coordinates x,y which lie on the tangent. The easiest point is where the tangent meets the curve. We know x = 2 so plugging that into the curve equation gives y = 3(2^2) + 4 = 16. Now we have values of x,y,m we can find c. c = 16 - 12*2 = -8. Therefore the final answer is y = 12x - 8

Answered by Maths tutor

5123 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

f(x) = 2 / (x^2 + 2). Find g, the inverse of f.


solve the inequality x^2+4x-21>0


The straight line L1 passes through the points (–1, 3) and (11, 12). Find an equation for L1 in the form ax + by + c = 0, where a, b and c are integers


A circle with centre C has equation x^2 + y^2 + 2x + 6y - 40 = 0 . Express this equation in the form (x - a)^2 + (x - b)^2 = r^2. Find the co-ordinates of C and the radius of the circle.


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