Differentiation Flashcards
How do you find f’(x) from f(x)=x^n?
F’(x)=nx^n-1
Differentiate f(x)=x^2
F’(x)=2x
Differentiate y=x^2
Dy/dx = 2x
If f(x)= bx then what is f’(x)?
b
If f(x)= c then what is f’(x)?
0
To find the equation of a tangent to a curve what do you first need to do?
Find the gradient ‘m’ of the curve via differentiation
What’s the equation of a straight line?
y-y1=m(x-X1)
What is the normal?
The line PERPENDICULAR (don’t for get that lol) to the tangent!!!!
How do you find the tangent/normal to a curve? (3steps pls)
1- differentiation
2- coordinates
3- substitution
What is a stationary point/turning point of a curve?
When the gradient equals 0
State dy/dx when it is a maximum:
Dy/dx >0
Dy/dx =0
Dy/dx <0
/-\
State dy/dx in terms of minimum:
Dy/dx <0
Dy/dx =0
Dy/dx >0
_/
What table could you use to find out if the stationary point is a minimum or a maximum?
x | -1 of X | X | + 1 of X
Dy/dx | | 0 |
Max/min| | - |
If the function is increasing what is the gradient?
Positive
If the gradient is decreasing what is the gradient?
Negative
