Question

consider the function and then use calculus to answer the questions that follow 1 1/x 5/x^2 1/x^3 (a) Find the interval(s) where the function is concave up. (Enter your answer in interval notation,do not round). (b) Find the interval(s) where the function is concave down. (Enter your answer in intervalnotation, do not round).

Answer 1

a)

b)

Explanation:

From the question we are told that

The Function

Generally the differentiation of function f(x) is mathematically solved as

Therefore

Generally critical point is given as

Generally the maximum and minimum x value for critical point is mathematically solved as

Where

Maximum value of x

Minimum value of x

Therefore interval of increase is mathematically given by

Therefore interval of decrease is mathematically given by

Generally the second differentiation of function f(x) is mathematically solved as

Generally the point of inflection is mathematically solved as

Therefore inflection points is given as

a)Generally the concave upward interval X is mathematically given as

b)Generally the concave downward interval Y is mathematically given as