What is the tangent line to the curve y = x^3+4x+5 at the point where x = 2?

First, we must find the value of y when x = 2.

y = x3+4x+5 = (2)3+4(2)+5 = 21

Then we must find the gradient of the tangent line. This can be done by differentiating y with respect to x and substituting x = 2.

dy/dx = 3x2+4 = 3(2)2+4 = 16

Now that we have a point (2,21) and the gradient (m = 16) of our tangent line, we can find the equation of the tangent using the formula:

y-y= m(x-x1)

y-21 = 16(x-2)

y = 16x-32+21

Thus y = 16x-11 is the equation of the tangent

OT
Answered by Oliver T. Maths tutor

13242 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Integral of (cos(x))^2 or (sin(x))^2


How do I find the co-ordinates of a stationary point of a given line and determine whether it is a minimum or a maximum point?


solve 2cos^2(x) - cos(x) = 0 on the interval 0<=x < 180


Find the equation to the tangent to the curve x=cos(2y+pi) at (0, pi/4)


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