calculus
posted by Jin on .
Consider the function
f(x)=–3x3–1x2+1x+1Find the average slope of this function on the interval (–2–1).
By the Mean Value Theorem, we know there exists a c in the open interval (–2–1) such that f(c) is equal to this mean slope. Find the value of c in the interval which works
I found the mean which is 17 but I can't get the C. I don't know what im doing wrong

f(1) = 311+1 = 2
f(2) = 19
slope = (219)/1 = 17 agree
f'(x) = 9 x^2  2 x + 1
for what values of x is that 17?
9 x^2  2 x + 1 = 17
9 x^2 + 2 x  18 = 0
x = [2 +/ sqrt (4+648)]/18
= 1.3 or 1.53
1,53 is in the domain
check it by calculating
f'(1.53)