Question

Find the sum of the values satisfying the Mean Value Theorem given the function
f(x)=(x^3/3)-2x^2+3x+4
on the interval 0≤x≤4
@3mar do you think you could help me?

Answer 1

What do you know about "the Mean Value Theorem"?

Answer 2

Not much...
I know that the slope is equal to f(b)-f(a)/b-a

Answer 3

That is right ..
and this is the complete view of it!

http://www.sosmath.com/calculus/diff/der11/der11.html

Can you plug in your values of f(0) and f(4) and find it out!?

Answer 4

f(0)=4
and
f(4)= 16/3

Answer 5

and the ratio of \(\frac{f(b)-f(a)}{b-a}\)?

Answer 6

if that is your original function!!
\[\LARGE f(x)=\frac{ 1 }{ 3 } x^3-2x^2+3x+4\]

Answer 7

1/3?
and yes that's the original function

Answer 8

Very good!
So you mean that:
\[\Huge \frac{ f(4)-f(0) }{ 4-0 }=\frac{ \frac{ 16 }{ 3 } -4}{ 4-0 }=\color{Coral}{\frac{ 1 }{ 3 }}\]

am I right?

Answer 9

yes

Answer 10

Congratulations!
You hit the right target!

Answer 11

yay! thanks! could you help me with 2 more please?

Answer 12

Of course.
With my pleasure!