Find the average or mean slope of the function on a interval

[jose1]

Hello
I have the exercise below:
Consider the function f(x)=1−8x2 on the interval [−5,6]. Find the average or mean slope of the function on this interval, i.e.

[f(6)-f(-5)]/[6-(-5)]

according to the theorem of laGrange

the slope in a continues function which is derivable in an interval should equal to f'(c), So

[f(6)-f(-5)]/[6-(-5)] is equal to 8. According to the site this is wrong?

and

f'(x) = -16x. So, -16x=8 is x=-1/2. According to the site this is wrong?

Could you please give me some advice? where is my mistake?
I will appreciate any help

Thanks

 

[Opalg]

Hello
I have the exercise below:
Consider the function f(x)=1−8x2 on the interval [−5,6]. Find the average or mean slope of the function on this interval, i.e.

[f(6)-f(-5)]/[6-(-5)]

according to the theorem of laGrange

the slope in a continues function which is derivable in an interval should equal to f'(c), So

[f(6)-f(-5)]/[6-(-5)] is equal to 8. According to the site this is wrong?

and

f'(x) = -16x. So, -16x=8 is x=-1/2. According to the site this is wrong?

Could you please give me some advice? where is my mistake?
I will appreciate any help

Thanks

Hello jose, and welcome to MHB.

The answer to the question is $\dfrac {f(6) - f(-5)}{6 - (-5)}$. If you check your calculation for that, you should find that it gives the value $-8$, not $8$.