Derivative — Precalculus, what it means and where it is taught
The slope of the tangent, written f'(x) or dydx.
Taught in Precalculus.
Where it is taught
What it rests on
Work through these first if this one does not settle.
Practise this idea
3 questions in the course bank use Derivative, in Rates of Change & the Derivative.
Problem 1
For y=x2-8x+1, at what x is the tangent horizontal?
Worked answer
4
2x-8 = 0
x = 4
Problem 2
For y=x3-3x, find the positive x where the tangent is horizontal.
Worked answer
1
3x2-3 = 0
x2 = 1, so x = 1 or -1
Problem 3
At a point the derivative is negative. What is the function doing?
- Falling
- Rising
- Flat
- Undefined
Worked answer
Falling
A negative slope means the curve is going down