# math

Let f be the function with f(0) = 1/ (pi)^2, f(2) = 1/(pi)^2, and the derivative given by f'(x) = (x+1)cos ((pi)(x)). How many values of x in the open interval (0, 2) satisfy the conclusion of the Mean Value Theorem for the function f on the closed interval [0, 2] ?

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. The function is the same at x = 0 and x = 2
so the mean slope is zero.
Therefore what it is asking is:
How many times is f'(x) = (x+1)cos (pi x) = 0
between pi x = 0 and pi x = 2 pi
well (x+1) is always a positive number in that interval
so
How many times is cos theta = 0 between theta = 0 and theta = 2 pi ????

1. 👍
2. 👎
3. ℹ️
4. 🚩
👤
Damon
2. It is just pretending to be difficult.

1. 👍
2. 👎
3. ℹ️
4. 🚩
👤
Damon
3. So would the answer be pi/2 and 3pi/2?

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### calc

d/dx integral from o to x of function cos(2*pi*x) du is first i do the integral and i find the derivative right. by the fundamental theorem of calculus, if there is an integral from o to x, don't i just plug the x in the function.

2. ### calc

i did this problem and it isn't working out, so i think i'm either making a dumb mistake or misunderstanding what it's asking. A particle moves along the x axis so that its velocity at any time t greater than or equal to 0 is

3. ### Calculus

Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis

4. ### calculus 2

Suppose that you can calculate the derivative of a function using the formula f'(x) = 4f(x) + 2x. If the output value of the function at x= 4 is 2 estimate the value of the function at 4.013

1. ### Calc AB

Remember that f(x) must be one-to-one (only one y-value for each x-value) over the domain where f β1(x)is defined as a function. So, in some cases you must restrict the domain of f(x) so that it's one-to-one. There might be more

2. ### Calculus

Suppose that f is a differentiable function with derivative π'(π₯) = (π₯ β 3)(π₯ + 1)(π₯ + 5). Determine the intervals of x for which the function of f is increasing and decreasing.

3. ### Calculus. I need help!

Write the composite function in the form f(g(x)). [Identify the inner function u=g(x) and the outer function y=f(u).] Then find the derivative dy/dx. y=βsinx β is square root.

4. ### Calculus

1. is the derivative of the function f(x)=5e^(4x-9z) f'(x)= -25e^(4x-9z)? 2. Is the derivative of the function f(x)=e^(2x)-e^(-2x) f'(x)=2e^(2x)+2e^(-2x)? 3. If f(x)=e^-x^-1, would f'(2)=-1/4e^(1/4)?

1. ### Calculus

f(x) = x2 + 2x - 1 Compute the derivative (that is, the derivative function) by evaluating the limit. Show your work. (Notice that for the function k(x), youβll have to compute the limit differently depending on whether x < 2 or

2. ### Calculus

How many critical points does the function f(x) = [(x-2)^5][(x+3)^4] have? A. 1 B. 2 C. 3 D. 5 E. 9 --- Ok, these are my thoughts on this question: My impulse was to do derivative of the function. However, if I'm going to set the

3. ### inverse

If f(x)=cosx + 3 how do I find f inverse(1)? Thanks y = cos(x) + 3 the inverse of this is x = cos(y) + 3 solve for y and you have your inverse The cos function only has a range of [-1,1], so the range of f(x) is [2,4]. this means

4. ### Calculus c

Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis