application of derivate

Question 1

slope of tangent

Answer 1

dy/dx

Question 2

eqn of tangent

Answer 2

y-y1=dy/dx(x-x1)

Question 3

for horizontal tangent

Answer 3

dy/dx=0

Question 4

for vertical tangent

Answer 4

dx/dy=0

Question 5

angle bw curves or lines

Answer 5

tan@=m1-m2/1+m1m2

Question 6

maximum value

Answer 6

dy/dx=0 , then put x in d2y/dx2 and its negtive

Question 7

minimum value

Answer 7

dy/dx=0 , then put x in d2y/dx2 and its positive

Question 8

for pt. of minima

Answer 8

d2y/dx2>0

Question 9

pt of maxima

Answer 9

d2y/dx2<0

Question 10

for greatest value and least value

Answer 10

first step f’(x)=o

Question 11

rolles theorm

Answer 11

conditions 
should be continuous 
should be defrentiable 
f(a)=f(b)
then f'(c)=o

Question 12

lvmt

Answer 12

conditions
should be continuous
should be defrentiable
the f’(c)=f(B)-f(a)/b-a