12 differentiation Flashcards
How to you define the gradient of a curve at a given point?
The gradient of the tangent to the curve at that given point.
What is an increasing function?
When the gradient of a line is positive.
What is the gradient at a turning point?
0
What is it called when their is neither a min or max point on a curve, but the gradient is still 0 at a point?
Stationary point of inflection.
What does lim h->0 mean?
h is getting smaller to a point where it is negligible.
What is the algebraic equation for a tangent.
F(x+h) - f(x) / h
See OneNote differentiation page for working.
What is x to the power of -2 equal to?
1/x(squared)
How do you differentiate something?
take the power of ‘x’, multiply the coefficient of ‘x’ by it, then reduce the power by 1.
What is f’(x)?
The differentiated version of f(x)
What is the normal?
The line that goes through the same point as another line, while being perpendicular to it.
When f’(x) > 0 is it an increasing or decreasing function?
increasing function.
What is the second derivative?
A term differentiated twice.
How to find if a stationary point is a min or max point? (No second derivative)
pick two x coordinates either side of the point and find the gradient.
How to find if a stationary point is min or max? (Using second derivative)
If second derivative is positive it’s a min point, if it is negative it is a max point.
