For the problem y=-(-x^2/2)-2x; [-3,1], find the value of c that satisfies the Mean Value Theorem.

We seek to verify the Mean Value Theorem for the function

f(x)=3x2+2x+5

on the interval

[−1,1]

The Mean Value Theorem, tells us that if

f(x)

is differentiable on a interval

[a,b]

then ∃

c∈[a,b]

st:f'(c)=f(b)−f(a)b−a

So, Differentiating wrt

x

we have:

f'(x)=6x+2

And we seek a value

c∈[−1,1]

st: f'(c)=f(1)−f(−1)1−(−1)

∴6c+2=(3+2+5)−(3−2+5)2

∴6c+2=42

∴6c+2=2

∴6c=0

∴c=0

maybe i can