Let f be the function given by f(x)=x^3-3x^2. Find all values of c that satisfy the conclusion of the Mean Value Theorem of differential calculus on the closed interval [0, 3]. (Answer: 2) ( I know that f'(x)=3x^2-6x and f'(c)=3. But what to do next?)

Question

anonymous · Answer

find the slope from 0 to 3, then set f'(x) = that slope, and solve for c

anonymous · Answer

how to find that slope?

anonymous · Answer

slope fomula

anonymous · Answer

So the slope is 3?

mathmale · Answer

Dear Idealist, Your interval is [0,3].  Evaluate the given function at both of those x values.  If you like, graph the resulting points.  Then, as sourwing suggests, use the slope formula to determine the slope of the line that connects these two points.  Note that this is a "secant line."

mathmale · Answer

Before I answer that:  Please type the two points that you've obtained.