# calculus

posted by .

Consider the function

f(x)=–3x3–1x2+1x+1Find the average slope of this function on the interval (–2–1).
By the Mean Value Theorem, we know there exists a c in the open interval (–2–1) such that f(c) is equal to this mean slope. Find the value of c in the interval which works

I found the mean which is -17 but I can't get the C. I don't know what im doing wrong

• calculus -

f(-1) = 3-1-1+1 = 2
f(-2) = 19
slope = (2-19)/1 = -17 agree

f'(x) = -9 x^2 - 2 x + 1
for what values of x is that -17?
-9 x^2 - 2 x + 1 = -17

9 x^2 + 2 x - 18 = 0

x = [-2 +/- sqrt (4+648)]/18
= 1.3 or -1.53

-1,53 is in the domain

check it by calculating
f'(1.53)

## Similar Questions

1. ### Calc, Mean Value Theorem

Consider the function : 3x^3 - 2x^2 - 4x + 1 Find the average slope of this function on the interval. By the Mean Value Theorem, we know there exists a "c" in the open interval (-2,3) such that f'(c) is equal to this mean slope. Find …
2. ### calculus

Consider the function f(x)=4sqrtx+5 on the interval [4,5]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval (4,5) such that f'(c) is equal to …
3. ### calculus

Consider the function f(x)=6sqrt(x)+1 on the interval [3,5] . Find the average or mean slope of the function on this interval. I FOUND THIS: (6sqrt(5)-6sqrt(3))/2 By the Mean Value Theorem, we know there exists a c in the open interval …
4. ### CALCULUS!

Consider the function f(x)=4x^3–2x on the interval [–2,2]. Find the average or mean slope of the function on this interval. __14__ By the Mean Value Theorem, we know there exists at least one c in the open interval (–2,2) such …
5. ### calculus

Consider the function f(x)=3x^2 – 5x on the interval [-4,4]. Find the average slope of the function on this interval. By the mean value theorem, we know there exists at least one c in the open interval (-4,4) such that f’(c) is …
6. ### calc

consider the function f(x)=x^3 - x^2 - 3x -2. find the average slope of this function on the interval (-2,3). by the mean value theorem, we know there exists a c in the open interval (-2,3) such that f'(c) is equal to this mean slope. …
7. ### math

Consider the function f(x)=–2x^3–3x^2+2x–2 Find the average slope of this function on the interval (2,6). ?
8. ### math

Consider the function f(x)=2sqrtx+4 on the interval [2,8]. Find the average or mean slope of the function on this interval. ?