Consider on . At which interior point of the interval does the derivative of equal…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Consider

f(x)=x^{3}-6x^{2}+9x

[0,3]

. At which interior point of the interval does the derivative of

f

equal the average rate of change of

f

[0,3]

? (a)

x=2

(b) No such point exists in

(0,3)

(c)

x=1

(d)

\displaystyle x=\frac{3}{2}