Question

given the curve y=e^(-2x) - 3x
the curve crosses x-axis at A(a,0) and y-axis at B(0,1), O is the origin. prove that 6a^2+3a<1

Answer 1

@shubhamsrg @jim_thompson5910

Answer 2

@Zarkon @Chlorophyll

Answer 3

from your hypotheses:
\[ \large 0=e^{-2a}-3a \]
and
\[ \large 1=e^{-2\cdot0}-3\cdot0 \]
(this last one is obvious)

Answer 4

yea, i know that... but i stuck to prove that 6a^2+3a<1

Answer 5

@ganeshie8 @ash2326 @UnkleRhaukus