MHB Maxima, minima, and the mvt application

T Botha
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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.
 
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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.
 

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