Answer:
b. x=2,3,4
c.
x=2 is a local minimum
x=3 is a local maximum
x=4 is a local minimum
d.
Explanation:
a. You have the function
to find the intervals you have to take into account the roots of f(x), in this case you have the roots
- for x < 2, for example x=1:
f(x) decreases from infinity to zero
- for 2 < x < 4, for example x=3:
between x=2 and x=3 f(x) increases. But between x=3 and x=4 f(x) decreases because f(4)=0.
- for x > 4:
f(5)>0
f(x) increases for x > 4.
b. You have to compute the derivative to find local minima and maxima
and by taking f'(x)=0:
Local minima and maxima are found by evaluating the roots of f'(x) in the second derivative f''(x)
Hence
x=2 is a local minimum
x=3 is a local maximum
x=4 is a local minimum
c.
to find the concavity you have to find the inflection points
Hence:
for -infinity < x < x1 --> concave up
for x1 < x < x2 --> concave down
for x2 < x < infinity --> concave up
d.