Find a point c satisfying the conclusion of the Mean Value Theorem for the following function and interval.
f(x)=x^(-2) [1,5]

Question

Find a point c satisfying the conclusion of the Mean Value Theorem for the following function and interval.
f(x)=x^(-2)                 [1,5]

laddiusmaximus · Answer

I know to use f(b)-f(a)/b-a  becomes (1/5-1/1)/(4)

laddiusmaximus · Answer

which equals -16/5

laddiusmaximus · Answer

im lost after this

zarkon · Answer

$$f(5)=5^{-2}=\frac{1}{25}$$

zarkon · Answer

you need to solve $$\frac{f(5)-f(1)}{5-1}=f'(c)$$ for $c$

laddiusmaximus · Answer

still lost

experimentx · Answer

find dy/dx ... put it to the value calculated from above  and solve for x

experimentx · Answer

dy/dx = ((1/25) - 1)/(5-1) ... solve for x

experimentx · Answer

experimentx · Answer

2.0374 (( [1, 5]

anonymous · Answer

$$ \frac{f[5]-1}{5-1}= f'[c]
$$

$$ -\frac{6}{25}= -\frac 2 {c^3}
$$
$$3 c^3= 25
$$

$$c = (\frac {25}3)^{1/3}$$