How do you differentiate the curve y = 4x^2 + 7x + 1? And how do you find the gradient of this curve?

To begin with, this question requires you to differentiate the curve y = 4x2 + 7x +1 in order to find the gradient. To differentiate this function y in respect to x, we need to reduce the powers by one, for example in this question dy/dx (the gradient line) will become:dy/dx = (42)x2-1 + (71)x(1-1) + (10), which becomes dy/dx = 8x +7. This is the gradient of the curve, so in order to find the gradient of the curve at a specific point, we need to substitute the value we are given into dy/dx. For example, if you were asked to find the gradient of the curve at the point (1, 12), in this case x = 1 and y = 12, so when you subsitute x = 1 into dy/dx, the gradient = 15, as dy/dx = 81 +7. If the question was asking you to find the gradient when x = 5, dy/dx = 8*5 +7 = 47. Because this is a curve, the gradient is not the same at each point, as opposed to a straight line. Once you have found the value of dy/dx, you can use it to find the tangent to the curve at a point, or the normal (perpendicular to the tangent) to a curve at a given point.

Answered by Katie S. Maths tutor

3660 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate "sin(2x)"


The straight line with equation y=3x-7 does not cross or touch the curve with equation y=2px^2-6px+4p, where p is a constant.(a) Show that 4p^2-20p+9<0 (b) Hence find the set of possible values for p.


integrate 1/((1-x^2)^0.5) between 0 and 1


How do I differentiate (2x+1) / (3x^2 - 5)?


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