Saturday

December 20, 2014

December 20, 2014

Posted by **Michael** on Friday, November 10, 2006 at 2:53pm.

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 the two values of "c" in the interval which work.

The average is 15, i know thats right.

f(b) - f(a)

-------------

b - a

not sure how to get the second part of the question tho.

You just need to calculate the derivative of the function. It is:

f'(x)= 6x^2 - 4x - 4

You then solve the equation

f'(c) = 15 --->

6c^2 - 4c - 4 = 15

wouldn't the derivative be:

f'(x)= 9x^2 - 4x - 4 ?

when i set that equal to 15, then i would get 7, and 19/3, both of which are not in the interval.

Yes, you are right!

Yes, you are right!

Let me see:

9x^2 - 4x - 4 = 15 -->

9x^2 - 4x - 19 = 0 --->

x = 4/18 +- 1/18*Sqrt[4^2 + 4*9*19]

So the solutions are x = 1.69 and

x = -1.247 which are inside the interval

Oh i c what i did wrong, i wasnt setting equation to zero. Thanks!

**Answer this Question**

**Related Questions**

calc - consider the function f(x)=x^3 - x^2 - 3x -2. find the average slope of ...

calculus - Consider the function f(x)=–3x3–1x2+1x+1Find the average slope of ...

math - Consider the function f(x)=2sqrtx+4 on the interval [2,8]. Find the ...

calculus - Consider the function f(x)=4sqrtx+5 on the interval [4,5]. Find the ...

math - Consider the function f(x)=–2x^3–3x^2+2x–2 Find the average slope of this...

Calculus Please help! - Consider the function f(x)=4sqrt(x)+4 on the interval [2...

CALCULUS! - Consider the function f(x)=4x^3–2x on the interval [–2,2]. Find the...

calculus - Consider the function f(x)=6sqrt(x)+1 on the interval [3,5] . Find ...

Calculus - Verify the hypothesis of the mean value theorem for each function ...

calculus - Consider the function f(x)=3x^2 – 5x on the interval [-4,4]. Find the...