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MTH101 Assignment 1 Solution and Discussion

ASSIGNMENT#1
Fall 2019Total marks: 10
Due Date: 30th December, 2019DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
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• Also remember that you are supposed to submit your assignment in Word format any other like scan images etc will not be accepted and we will give zero marks correspond to these assignments.Question:
If Find the intervals where the given function is Increasing
 Decreasing
 Concave up
 Concave down respectively.
Also find the point of inflection for the given function.


Q: If Find the intervals where the given function is
Solution:
Increasing
f(x)=x327x
After Taking Derivative
f `(x)=3x227
Function will increase if it is greater than zero
f `(x)=3x227>0
3x227>0
x29>0
x2>9
After taking square root
x>3
So, function increase on (3,∞)
Decreasing
f(x)=x327x
Take Derivative
f `(x)=3x227
Function will decrease when it is less than zero
f `(x)=3x227<0
3x227<0
x29<0
x2<9
After taking square root
x<3
So, function decrease on ( ∞, 3)
Concave up
f(x)=x327x
After Taking Derivative
f `(x)=3x227
After taking second derivative
f ``(x)=6x
f ``(x)=6x>0
6x>0
x>0
So, it is concave up on (0,+∞)
Concave down
f(x)=x327x
After Taking Derivative
f `(x)=3x227
After taking second derivative
f ``(x)=6x
f ``(x)=6x<0
6x<0
x<0
So, it is concave down on ( ∞,0)
POINT OF INFLECTION
f(x)=x327x  (1)
After Taking Derivative
f `(x)=3x227
After taking second derivative
f ``(x)=6x
f ``(x)= 6x =0
6x=0
x=0
Put this in (1)
f(0)=(0)3 27(0)
f(0)=0
So, inflection point is (0 , 0)