C12 Differentiation Flashcards
How is the gradient function or derivative of the curve y=f(x) written?
dy/dx or f’(x)
What can the gradient function be used to find?
The gradient of the tangent to the curve for any values of x
The equation of a straight line:
y-y1=m(x-x1)
Where y1 and x1 are coordinates
How do you find the equation of the normal
The normal is perpendicular to the curve
So use negative reciprocal (of the tangent)
Mn= -1/Mt
What’s an increasing function?
Its gradient is always greater than 0
What’s a decreasing function?
Its gradient is always less than 0
How can you show that a function is greater than zero or less than zero
Completing the square
Where is the stationary point on a graph
Where it’s gradient is equal to 0
Turning points
What’s a point of inflection
Where the curve changes from convex to concave (or vise versa)
How can u tell if a stationary point is a max/min point or a point of inflection?
You could check the values of the gradient just before and after the stationary point
Use the second derivative (if greater than 0 then it’s increasing of negative then it’s decreasing, and if it equals 0 then it’s a point of inflection)
What does dy/dx mean
The rate at which y changes with respect to x
