5.3 Differentiating polynomialsIB Maths: Applications and Interpretation HL: Flashcards

What these 12 flashcards ask

What is the derivative of ax^n?
What is the derivative of kx?
What is the derivative of a constant?
Differentiate 5x^4.
Differentiate x^{-3}.
Differentiate \frac{6}{x}.
How do you differentiate a sum of terms?
Two notations for the derivative of y=f(x)?
How do you find the gradient of y=f(x) at x=a?
What does f'(x) measure in a modelling context?
Differentiate (2x+1)(x-3).
How do you find x where the gradient equals k?

Exam questions on 5.3 Differentiating polynomials

A function is defined by $f(x)=4x^3-6x^2+5x-9$ .
Find the values of $x$ at which the gradient of the graph of $f$ is $5$ .2 marks
A function is defined by $g(x)=3x^2+\frac{4}{x}-\frac{2}{x^2}$ , for $x\neq0$ .
Find $g'(-1)$ and state whether $g$ is increasing or decreasing at $x=-1$ .2 marks
The cost, $C$ AED, of producing $x$ items in a day is modelled by $C(x)=0.5x^3-6x^2+40x+200$ , for $0<x\le20$ . The rate of change of cost, in AED per item, is given by $C'(x)$ .
(i) Find $C'(x)$ . (ii) Find the rate of change of cost when $10$ items are produced.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).