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

The average is 15, i know that's 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 wasn't setting equation to zero. Thanks!

1. 👍
2. 👎
3. 👁

Similar Questions

1. Math (Secant Lines)

Consider the function f(x)=sqrt(x) and the point P(4,2) on the graph of f? -Consider the graph f with secant lines passing through p(4,2) and Q(x,f(x)) for x-values 1, 3, and 5. -Find the slope of each secant line -Use the results

2. Math

Find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. f(x) = 4x3 − 3x2, [−1, 2]

3. slope

Find the slope of the line passing through the given points using the slope formula. Enter the slope in simplest form. Describe the slope as positive, negative, zero, or undefined. (8,2) and (15,9) my answer = 1 the slope is

4. College algebra!

For the linear function f(x) = 5x + 3 (a) Determine the slope and y-intercept (b) Use the slope and y-intercept to graph the linear function. (c) Determine the average rate of change of the function (d) Determine whether the

1. Algebra 1

Question 9 Examine the graph of f(x) f ( x ) and the table that contains values of g(x). g ( x ) . Curve f of x approaches Y equals negative 7 on the left and positive infinity on the right. It passes through points (0, negative

2. calculus

1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))? 2. Find the derivative of f(x) = |x + 2| at the point (1, 3) 3. Find f '(x) for f(x) = -2x3 + 3x2 - x + 15. 4.

3. calculus

1. Find the average value have of the function h on the given interval. h(x) = 2 cos4(x) sin(x), [0, π] 2. Consider the given function and the given interval. f(x) = 6 sin(x) − 3 sin(2x), [0, π] (a) Find the average value fave

1) The linear function f(x) contains the points (-10, -29) and (-2, 83). If g(x) = 25x - 50, which statement is true? A. The functions f(x) and g(x) both have positive slopes.

1. math

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

2. math

Which statement correctly describes the slope of the linear function that is represented by the data in the table? x y 8 –8 8 –4 8 0 8 4 8 8 The slope is positive. The slope is negative. The slope is zero. There is no slope.

3. trigonometry

An object is attached by a string to the end of a spring. When the weight is released it starts oscillating vertically in a periodic way that can be modeled by a trigonometric function. The object's average height is −20 cm