Maxima, minima, and the mvt application

[T Botha]

Hi there

I'm prepping for a big test tomorrow and I'm really struggling with this question:If f′′(x)≥−1, x belongs to (−15,15), and f′(1)=3, find the interval over which x is definitely increasing.I'm struggling with substitution because I just don't seem to have enough values. Is there a formula that gives an answer? Please let me know.

:( this is making me so sad.

 

[HallsofIvy]

Since $$f''(x)\ge -1$$, $$f'(x)\ge -x+ C$$. Since f'(1)= 3, we know that C can be as large as 4. If $$f'(x)\ge -x+ 4$$ it will be positive for x less than 4.