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
When the second derivative is positive what is the stationary point?
Minimum
When the second derivative is negative what is the secondary point?
Maximum
What is a point of inflection?
_/ like a cubic graph basically
/
What is the notations for the second derivative?
D^2/dx^2 or f”(x)
D^2/dx^2>0 what is it?
Minimum
D^2/dx^2<0 what is it?
Maximum
When a question says the rate or in relation to or with respect to what do you do?
D I F F E R E N T I A T E
