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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).