Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
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Thank you for everything!!!!!!! bob bundy!!!!!! plus congrats to owner..admins..moderators etc. for this great site! cheers!
The square bracket means include the endpoint. It seems I am assuming too much. If it doesn't say strictly, I concede the argument.
wow! they are the same indeed! I feel sooooo much better now!
But the book shouldn't be saying less than and equal to because the graph has a turning point when = so dy/dx = 0
So the value of the function isn't getting bigger.
Your approach seems wonderful!!! and according to me correct.. but why does the book i have give another..but very similar answer?.. it says x<or=-1/2*ln3 Is it the same but i'm missing smth??
My post 4 may have been missed as bobbym and I posted together.
Hi bobbym! I took a look at the graph in wolframalpha or smth..but it won't help on my future exams.. if i do not know how to find the answer on my own.
OK, here we go.
e^x is always positive so you need
log base e is an increasing function so the inequality holds if you take logs
...how we find the interval where the function e^x-e^(3x) is increasing... the derivative is e^x[1 - 3e^(2x)]. I have the answer but I feel lost..