13/14/15 - differentiation/ integration

Question 1

gradient is the

Answer 1

rate of change of x with respect to y

Question 2

differentiation notation

Answer 2

dy/dx
f’(x)

Question 3

differentiation

Answer 3

y= ax^n
dy / dx = anx ^n-1
times by the power of x then -1 from the power
eg y = x^3
dy / dx = 3x^2

Question 4

second order derivative

Answer 4

differentiate twice
f’‘(x)
d^2y/ dx^2
rate of change of the gradient of a function

Question 5

summing functions

Answer 5

is y = f(x) + g(x)
dy/ dx = f’(x) + g’(x)

Question 6

a function is increasing if

Answer 6

dy/dx >0
and decreasing if its <0

Question 7

a point is a max / min if

Answer 7

max if f’‘(x) <0
min if f’‘(x) >0
if second order deriveative = 0 could be max/ min or inflection point

Question 8

integration

Answer 8

S y= ax^n
dx = a/(n+1) x ^n+1 + c
add one to the power and divide by new power

Question 9

integration notation

Answer 9

S (equation) dx = (integrated form) +c
if definite write in [ ] with limits outside