GCSE Geography AQA 8035

Know that the gradient function $\dfrac{dy}{dx}$ gives the gradient of the curve and measures the rate of change of $y$ with respect to $x$

Know that the gradient of a function is the gradient of the tangent at that point

Differentiation of $kx^n$ where $n$ is an integer, and the sum of such functions

*Including expressions which need to be simplified first

Given $y = (3x+2)(x-3)$ work out $\dfrac{dy}{dx}$

Given $y = \dfrac{5}{x^3}$ work out $\dfrac{dy}{dx}$ *

The equation of a tangent and normal at any point on a curve

Increasing and decreasing functions

When the gradient is positive/negative a function is described as an increasing/decreasing function

Understand and use the notation $\dfrac{d^2y}{dx^2}$

Know that $\dfrac{d^2y}{dx^2}$  measures the rate of change of the gradient function

Use of differentiation to find maxima and minima points on a curve

*Determine the nature either by using increasing and decreasing functions or $\dfrac{d^2y}{dx^2}$ *

Using calculus to find maxima and minima in simple problems

*$V = 49x + \dfrac{81}{x} \quad x > 0$

Use calculus to show that $V$ has a minimum value and work out the minimum value of $V$ *

Sketch/interpret a curve with known maximum and minimum points