Mathematics 0580 · IGCSE · Differentiation

Differentiation — practice question

The table lists several values of $y = 2x^3 - 4x^2 + 3$.
(a(i))[3]

Fill in the missing entries in the table.

(a(ii))[4]

On the grid, sketch the graph of $y = 2x^3 - 4x^2 + 3$ for $-1 \leq x \leq 2$.

(a(iii))[3]

From your graph, determine the solution to $2x^3 - 4x^2 + 3 = 1.5$.

(a(iv))[1]

The equation $2x^3 - 4x^2 + 3 = k$ has just one solution on $-1 \leq x \leq 2$. Give one possible integer value of $k$.

(b(i))[1]

On the grid, sketch the tangent to the curve at $x = 1$.

(b(ii))[2]

Use your tangent to estimate the gradient of the curve when $x = 1$.

(b(iii))[2]

Write the equation of your tangent in the form $y = mx + c$.

Worked solution & mark scheme

This 16-mark question has a full step-by-step worked solution and mark scheme. One marking point: 3

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