Mathematics 0580 · IGCSE · Differentiation

Differentiation — practice question

Suppose $f(x)=\frac{x^2}{4}-\frac{4}{x}$, $x\neq0$.
(a)[2]

Fill in the table for $f(x)$.

(b)[3]

Using the same grid, sketch the graph of $y=f(x)$ for $0.5\le x\le6$.

(c)[3]

Draw an appropriate tangent and use it to estimate the gradient of the graph of $y=f(x)$ at $(-4,5)$.

(d)[1]

Fill in the table for $g(x)$.

(e)[4]

Using the same grid, draw the graph of $y=g(x)$ for $-4\le x\le -1$ and $1\le x\le4$.

(f(i))[1]

Use the graphs to determine the value of x when $f(x)=g(x)$.

(f(ii))[1]

State an inequality that shows the positive values of x for which $f(x)>g(x)$.

(g)[2]

Use algebra to determine the value of k.

Worked solution & mark scheme

This 17-mark question has a full step-by-step worked solution and mark scheme. One marking point: $-1$

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI