Question

Take three more groups of large numbers and do the exercise given above. 527864 ,95432 , 18950049 , 70002509​

Answer 1

Answer:

f′(x)f′(x) gives you the slope of ff in x

Quite easily, if f′(x)f′(x) is positive, f(x)f(x) increases. If f′

(x)f′(x) is negative, f(x)f(x) decreases.

We know that, for y∈R∗+y∈R∗+

0<y<1⇔ln(y)<00<y<1⇔ln(y)<0

ln(1)=0ln(1)=0

1<y⇔ln(y)>01<y⇔ln(y)>0

So we can write that

f′(x)>0⇔ln(x2x+1)>0⇔x2x+1>1f′

(x)>0⇔ln(x2x+1)>0⇔x2x+1>1

f′(x)<0⇔ln(x2x+1)<0⇔x2x+1<1f′

(x)<0⇔ln(x2x+1)<0⇔x2x+1<1

If x<−1