Nikhil Holt
2022-03-14
orangepaperiz7
Beginner2022-03-15Added 9 answers
Step 1
is concave downward for all
As Kim suggested a graph should make this apparent (See bottom of this post).
Alternately,
Note that
and checking for critical points by taking the derivative and setting to 0
we get
or
which simplifies (if ) to
At
Since is the only critical point (other than ) and f(x) decreases from to
it follows that decreses on each side of , so
is concave downward when
When we simplify note that
is a straight line and
remains a positive amount (namely above that line therefore f(x) iss not concave downward for
Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function
in derivative?
What is the derivative of ?
What is the limit of as ?
What is the derivative of ?
What is the derivative of ?
How to find as using l'Hospital's Rule?
What is the integral of ?
What is the derivative of ?
What Is the common difference or common ratio of the sequence 2, 5, 8, 11...?
How to find the derivative of ?
How to evaluate the limit as x approaches 0?
How to find derivatives of parametric functions?
What is the antiderivative of ?
How to evaluate: indefinite integral ?