calc
posted by matt on .
consider the function f(x)=x^3  x^2  3x 2. find the average slope of this function on the interval (2,3). by the mean value theorem, we know there exists a c in the open interval (2,3) such that f'(c) is equal to this mean slope. find the two values of c in the interval which work.

f(2) = 8
f(3) = 7
average slope = (7+8)/(3+2) = 3
f'(x) = 3x^2  2x  3
f'(c) = 3c^2  2c  3
3c^2  2c  3 = 3
3c^2  2c  6 = 0
c = (2 ± √73)/6
= (2 ± 6√2)/6
= 1/3± √2