Answer:
a. f is increasing in the interval and decreasing in the intervals
b. local maximum value of the function is 6, -250 and Local minimum value of the function is -250
c. inflexion points are
f is concave up in intervals and concave down in interval
Step-by-step explanation:
Given:
To find: interval on which f is increasing and decreasing, local minimum and maximum values of f, inflection points and interval on which f is concave up and concave down
Solution:
A function f is increasing in the interval in which and decreasing in the interval in which
If a function is increasing before a point and decreasing after that point, the point is said to be a point of local maxima.
If a function is decreasing before a point and increasing after that point, the point is said to be a point of local minima.
An inflection point is a point on the graph of a function at which the concavity changes. Put second derivative equal to zero as check if concavity changes at the points obtained. Such points are said to be points of inflexion.
A function f is concave up in the interval in which and concave down in the interval in which
a.
Observe the attached table.
So, f is increasing in the interval and decreasing in the intervals
b.
From the table,
a function f has a local maxima at and local minima at
So, local maximum value of the function is 6, -250
Local minimum value of the function is -250
c.
See the attached table
So, f is concave up in intervals
and concave down in interval
Also,
So, inflexion points are