#4.1
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 \(x\)
#4.2
Know that the gradient of a function is the gradient of the tangent at that point
#4.3
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 \(\dfrac{dy}{dx} \)
#4.4
The equation of a tangent and normal at any point on a curve
#4.5
Increasing and decreasing functions
When the gradient is positive/negative a function is described as an increasing/decreasing function
#4.6
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
#4.7
Use of differentiation to find maxima and minima points on a curve
Determine the nature either by using increasing and decreasing functions or \(\dfrac{d^2y}{dx^2} \)
#4.8
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 \(V\)
#4.9
Sketch/interpret a curve with known maximum and minimum points