Consider the function
f(x)=x^(3)-2x^(2)+8x
. (a) Is
f
continuous on the interval
-3,2
and differentiable on the interval
(-3,2)
? Explain your reasoning in words. (b) Using the results from (a), show there exists some real number
c
in the interval
(-3,2)
such that
f^(')(c)=17
. Clearly state your answer in words. (c) Find the value(s) of
c
from part (b).