Question

find the maximum value of f(X)=x÷1+4x+x^2​

Answer 1

two bar Twenty

Step-by-step explanation:

exist this show of school good hvff brbr ucch hhghhj chhe hun gn gunman mignon nhii iffy idk this idk this good thing good food tbhi gn CM xm so Osborn ignore hi bcom brunt brbr night gypsy hung hurts hybrid hhghhj

Answer 2

Step-by-step explanation:

The given equation is:

f(x)=1+4x+x2x

To find the extremum points we differentiate and equate it to zero

⇒f′(x)=(1+4x+x2)2(1+4x+x2)−(4+2x).x

⇒f′(x)=(1+4x+x2)21+4x+x2−4x−2x2

⇒f′(x)=(1+4x+x2)21−x2

f′(x)=0

⇒(1+4x+x2)21−x2=0

⇒1−x2=0

⇒x=±1

Now to find whether at the critical points we find a maxima or minima we use the second derivative test.

⇒f′′(x)=(1+4x+x2)4−2x(1+4x+x2)2−2(1+4x+x2)(4+2x)(1−x2)

⇒f′′(1)=(1+4+12)4−2x(1+4+12)2−2(1+4+12)(4+2)(1−12)

⇒f′′(1)=−622

⇒f′′(1)<0

⇒f′′(−1)=(1−4+(−1)2)4−2x(1−4+(−1)2)2−2(1−4+(−1)2)(4−2)(1−(−1)2)

⇒f′′(−1)=6

Hope u like the answer...

Please mark me as a brainliest