Question

A village in India is suffering from flood. Mr singh from New Delhi decieded to help them with food, clothes etc. So he collected some amount from different persons which is represented by x^4+2x^3+8x^2+12x+18. If there are X^2+5 number of persons who received this help and px+q is the amount left with Mr.Singh,find the value of p and q?


pls give full method plss

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