Question

Help me!

Answer 1

Find the values of c that satisfy the equation f(b)-f(a)/b-a= f prime(c) in the conclusion of the mean value theorem for the given function and interval. f(x)=9x+9/x [1/9, 9]

Answer 2

I told you how to find the answer. It is easy.

Answer 3

Take derivative of f(x) and solve for it equal to 0..

Answer 4

9-(9/x^2)

Answer 5

Rolle's Theorem sets the derivative = 0. The Mean Value Theorem locates the slope of a tangent line that is parallel to a secant of given endpoints.

In this case,you want to find the slope of the tangent line of the given function at point c that is parallel to the secant line of the given endpoints. Then find the value of c for the given function that gives you the equation of that line.

Answer 6

can you show me please?

Answer 7

f(b)-f(a)/b-a is formula for finding the slope of the secant.

Your endpoints are 1/9 and 9 (a = 1/9 and b = 9)

Substitute those in to the above formula, and that will be the slope of the secant AND the slope of the tangent line at point [c, f(c)]

Find f'(x) [you've already found f'(x), I see].

Now substitute c for x:

f'(c) = 9c - 9/c^2.

That is the slope of the tangent line at point c.

Set that equal to the slope of the secant line.

9c - 9/c^2 = slope of tangent line (which you solved for earlier).

Now solve for c!

Answer 8

I'm having difficulty finding the slope of the secant and tangent line

Answer 9

The slope of the secant is the same as the slope of any line:

m = y2 - y1/(x2 - x1)

In this case, the slope is given by f(b) - f(a)/(x - a)

Since f(x) = 9x + 9/x,

f(b) = 9(9) + 9/9 and
f(a) = 9(1/9) + 9/(1/9)
b - a = 9 = 1/9

Do the math! That is the slope of the secant.

Answer 10

b - a = 9 - 1/9

Answer 11

f(b)=82
f(a)=82

Answer 12

f(b)-f(a)=0

Answer 13

what am I doing wrong??