Differentiation Flashcards
What do these terms represent?
Rate of change, gradient function and derived function
Differentiation
How do you find the gradient of a tangent to a curve?
Differentiate the substitute x to find the gradient
How do you find the equation of the tangent to a curve?
- Differentiate and sub in x to find gradient
- find y by substituting x into original equation
- use y-b=m(x-a)
How do you sketch a graph of the derivative?
- f ’(x) = 0 at st. pts. To find roots
- find shape of graph using gradient
A function is increasing when…
f ’(x) > 0
A function is decreasing when…
f ’(x) < 0
A function is stationary when…
f ‘(x) = 0
How do you find stationary points of a function?
At stationary points f ‘(x) = 0
Differentiate and solve to find x values
Substitute back in to find y values
Use a nature table to determine the nature
How do you find where a function is increasing or decreasing?
Differentiate then use a nature table (or solve the inequality)
How do you show a function is ALWAYS increasing (decreasing)?
Differentiate then complete the square to show that f ‘(x) > 0 (f ‘(x) < 0) for all values of x
How do you find the solution to an optimisation problem?
Investigate stationary points (and end points if necessary)
What do you get if you differentiate distance?
Speed
What do you get if you differentiate speed?
Acceleration
What do you get if you differentiate sinx?
Cosx
What do you get if you differentiate cosx?
- sinx