Question

Let f be a function defined on an interval I and C I  , Let f be a
twice differentiable function at C than
1) X = c is a point of local maxima, if f c f c ' 0, "( ) 0     the value of
f c  is local maximum value of f
2) x=c is a point of local minima, if f c f c '( ) 0, " 0     , in this case
f c( ) is local minimum value of f.
3) If f’(c) = 0, f c "( ) 0  , then using first derivative test we can find
whether C is a point of local maxima, local minima or a point of
inflection, then
1) The local maximum of 4 3 2 f x x x x ( ) 3 4 12 12     is
a) - 7
b) + 20
c) 7
d) 15

1 mark

2) The shortest distance of the point (0,c) from the parabola
2 1
, 5
2

y x where c    is
a) 4 1 c 
b) 2 1
2
c 
c) 2 1 c 
d) 4 1
2
c 


3) x and y are two positive numbers such that their sum is 35, if
2 5 x y is maximum, then
a) x= 15, y = 20
b) x=10, y = 25
c) x =25, y = 10
d) None of the above

1 mark

4) The semi vertical angle of the cone of the maximum volume and of
given slant height is
a) 1 1
sin
3
      
b) 1
tan 2 
c) 1
tan 2 
d) 1
cot 2 

1 mark

5) A rectangular sheet of tin 45 cm by 24 cm is to be made into a box
without top by cutting off square from each corner and folding up the
flaps. Then the length of the side of the square to be cut off so that
the volume of the box is maximum.
a) 5 cm
b) 6 cm
c) 4 cm
d) 7 cm

Answer 1

Answer:

lol

Step-by-step explanation: