Finding Gradients (Edexcel IGCSE Further Pure Maths): Revision Note

Finding Gradients

How do I find the gradient of a curve at a point?

• The gradient of a curve at a point is the gradient of the tangent to the curve at that point

  • Find the gradient by substituting the value of $\mathit{x}$ at that point into the derivative of the curve

• For example, if $\mathrm{f}\left(x\right)=x^2+3x-4$

  • then $\mathrm{f}\text{'}\left(x\right)=2x+3$

  • the gradient of $y=\mathrm{f}\left(x\right)$ when $x=1$ is  ${\mathrm{f}}^{\text{'}}\left(1\right)=2\left(1\right)+3=5$

  • the gradient of $y=\mathrm{f}\left(x\right)$ when $x=-2$ is  ${\mathrm{f}}^{\text{'}}\left(-2\right)=2\left(-2\right)+3=-1$

• Your exam calculator cannot find a derivative function in terms of $x$

  • But it may be able to find the numerical value of a derivative at a point

  • You can use this to check your work