I have to use the Mean Value Theorem to find f'(c)
1. x^3+x on [1,2] the answer says c=1.5275...
2. x^4+2 on[-1,2] the answer says c=1.0772...
The entire directions state: Verify that the given function f satisfies the hypothesis of the MVT on the given interval [a,b]. Then find all numbers cbetween a and b for which: (f(b)-f(a)/b-a)=f'(c)
For 1, I found the deriv. which is 3x^2+1
Then applied 1 and 2 to the original equation and got 4 and 13 respectively.
plugged them into the MVT equation:13-4/2-1=9.
Then I plugged the 9 with the derivitive 3x^2+1 for it to become 3x^2+1-9=3x^2-8.
Made x stand by itself and got x = +or-(sqrt 8/3). and it doesn't add up to the answer.
For 2, Long story short, I did the exact same steps as in #1 and the result was the same.