Verify the applicability of the Intermediate Value Theorem (IVT) in the interval [0,5] and find the value c guaranteed by the theorem.

f(x)= x^2 + x - 1, f(c) = 11

Question

Verify the applicability of the Intermediate Value Theorem (IVT) in the interval [0,5] and find the value c guaranteed by the theorem.

f(x)= x^2 + x - 1, f(c) = 11

anonymous · Answer

i can tell you right off the bat that c is smack dab in the middle because you have a quadratic.  we can find it if you like

anonymous · Answer

please explain!

anonymous · Answer

ok what is 
$$f(5)$$?

anonymous · Answer

29

anonymous · Answer

yes and of course 
$$f(0)=-1$$

anonymous · Answer

so this graph contains the points 
$$(0,-1),(5,29)$$ and the slope between those two points is 
$$\frac{29+1}{5}=\frac{30}{5}=6$$

zarkon · Answer

?

anonymous · Answer

f(0) = -1
f(5) = 29 
and 11 is betwen those so IVT applies

anonymous · Answer

to find c you x^2 +x -1 = 11

anonymous · Answer

lorda mercy it says "intermediate value theorem" and i read "mean value theorem"  i should learn to read

zarkon · Answer

;)

anonymous · Answer

thank you all!

anonymous · Answer

i did this exact problem in my class

anonymous · Answer

in that case solve 
$$x^2+x-1=11$$which must have a solution because 
$$-1<11<29$$

anonymous · Answer

is that it?

zarkon · Answer

we should also mention that the function is a polynomial and is therefore continuous on the interval we are interested in