5.3 Differentiating polynomialsIB Maths: Applications and Interpretation SL: Mind map

Exam questions on 5.3 Differentiating polynomials

1. 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
2. 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
3. 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