https://www.khanacademy.org/math/differential-calculus/derivative-applications/mean_value_theorem/v/mean-value-theorem-1
the average slope is (f(1)-f(=1))/(2)=-16/2=-8 check that.
then the points are
f'=-8=3x^2-9
x^2=1/3
x=+- sqrt (1/3)
check: f'(sqrt1/3)=1-9=-8
f'(-sqrt1/3)=1-9=-8
Determine if the Mean Value Theorem for Integrals applies to the function f(x) = x^3 − 9x on the interval [−1, 1]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem.
Not quite sure how to do this one at all to be completely honest. Thank you for helping!
1 answer