12 - differentiation Flashcards
How would you write the gradient function
y = ……
dy/dx
How would you write the gradient function f(x) =
f’(x)
What is the formula for finding the derivative of first principles
lim h>0 [f(x+h) - f(x)] / h
What does differentiing an equation tell you
It tells you the gradient function
How do you differentiate
x^n = nx^n-1
ax^n = anx^n-1
What do you do if there is not an x term in the equation and you need to derive it
e.g f(x) = ax^2 +bx + c
Ignore the c and differentiate
f’(x) = 2ax + b
How do you know is f(x) is increasing or decreaing at any point
it is increasing if the value of f’(x) >= 0
It is decreasing if f’(x) <= 0
What is a staionary point
a point on a cure where f’(x) = 0
What are the 3 possible stationary points
Local maximum
Local minimum
Point of inflection
How can you identify if a stationary point is a local minimum
look at a small change beside the point of 0 in f’(x)It will be posistive, be 0 and then be negative
IF
f’‘(x) > 0 the point is a local minimum
How can you identify if a stationary point is a local maximum
look at a small change beside the point of 0 in f’(x)It will be negative , be 0 and then be positive
If
f’‘(x) < 0 the point is a local maximum
How do you identify the point if f’‘(x) = 0
Look at how the gradient changes around the stationary point
How do you identify a point of inflection
f’‘(x) = 0
AND
The gradients on both side of the point are positive
or
The gradients on both side of the point are negative
What is the gradient of a tangent to a curve
m
What is a gradient of a normal to a curve
-1/m
