calculus. Flashcards
What is the normal to the curve?
The line that is perpendicular to a curve at a certain point.
How are turning points found?
dy/dx is 0 at turning points.
What are increasing and decreasing functions?
An increasing function has a positive gradient for the specified x-values.
A decreasing function is the same but the gradient is negative.
What must dy/dx be if you want a positive function?
greater than 0.
What is a point of inflection?
A point where point on a curve at which the curve changes from being concave (concave downward) to convex (concave upward), or vice versa.
The sign of a gradient on either side doesn’t change.
If you want to classify a stationary point on a curve by using second derivatives, what does the sign of the answer mean?
If it is positive, a minimum point.
If it is negative, a negative point.
If it is 0, look at the gradient at either side.
How do you integrate?
Raise the power and divide the number in front by the raised power.
Remember to add a c at the end.
How would you find the area between a curve and the Y axis?
Rearrange the equation so that x is given in terms of y .
What is height in the trapezium rule?
The length of the sections along the x axis. It is the same for all of the trapeziums.
How do you find the correct y values for the trapezium?
Find the x values for the start of the divisions and use the equation of the line to find the correct y value for this x value. Do this for all the divisions and find all the y values.
When you have found all the y values for the trapezium rule, what do you do?
Add the second to start and second to last y values together and multiply by 2.
Then add the first and last y values to this.
Then multiply this by the height then by half.
