Consider the function F(x)=17(x^4)+13(x^3)+12(x^2)+7x+2. A) differentiate F(x) B)What is the gradient at the point (2,440)

A point of notation:
'#' is the beginning of a comment, we will use comments to note down thoughts and tricks at each stage of the problem
A) let f(x) denote the differential of F(x)
F(x)=17(x^4)+13(x^3)+12(x^2)+7x+2 # start by rewriting out the question so you can see clearly what you have to do
f(x)=(174)(x^3)+(133)(x^2)+(122)(x^1)+7 #differentiate term by term, x^4 first then x^3 and so on...
f(x)=56(x^3)+39(x^2)+24x+7 #finished. sanity check - does this make sense? why?
B) Let A be the point (2,4) #x=2 and y=440
sub in x=2 to f(x) #we have a function of x, and want to know what that function is at x=2
so we have; f(2)= 56*(2^3)+39*(x^2)+24*(2)+7f(2)=448+156+48+7f(2)=659

DW
Answered by Dylan W. Maths tutor

3068 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate the function y = cos(sin(2x))?


Take the polynomial p(x)=x^4+x^3+2x^2+4x-8, use the factor theorem to write p(x) as two linear factors and an irreducible quadratic. An irreducible quadratic is a quadratic that can not be factorised.


What is the difference between definite and indefinite integrals?


Two masses A and B, 2kg and 4kg respectively, are connected by a light inextensible string and passed over a smooth pulley. The system is held at rest, then released. Find the acceleration of the system and hence, find the tension in the string.


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