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Quadratic

b2-4ac=0
-Tangent to curve
-Equal roots

decreasing function
- dy/dx<0
-negative gradient
Otherwise, opposite

Curve lies above x-axis
Find min point, coordinates> 0
Or dy/dx=0, coordinates>0

Form equation from given roots
x2-sorx+por

1

Functions

No solutions
- b2-4ac<0

Stationary point
- dy/dx=0, inverse doesn't exist
If dy/dx0, no turning point, inverse exist.

For inverse of quadratic
- if the function is to the left of stationary point, sign of square root is -ve
Otherwise, opposite.

*g'(x) & g-'(x)
Dy/dx & inverse

Range of sin, cos
-deduce based on graph