Math Questions and Answers

Start Your Free Trial

f(x)=(x+4)/(sqrt(x^2+4) Find the exact value of the maximum of f and Find the exact value of x at which f increases most rapidly.

Expert Answers info

beckden eNotes educator | Certified Educator

calendarEducator since 2011

write562 answers

starTop subjects are Math, Science, and Business

f'(x)=(x+4)/sqrt(x^2+4)

f'(x)=(x+4)(d)/(dx)((x^2+4)^(-1/2))+(x^2+4)^(-1/2)(d(x+4))/(dx)

f'(x)=(x+4)(-1/2)(x^2+4)^(-3/2)(2x)+(x^2+4)^(-1/2)

f'(x)=-((x+4)x)(x^2+4)^(-3/2)+(x^2+4)(x^2+4)^(-3/2)

f'(x)=(4-4x))/(x^2+4)^(3/2)

f'(x)=0 when (4-4x)=0 x=1

Now we need to find if this is a minimum or maximum.

Since (x^2+4)>0 always we need to find out the signs of (4-4x)

(4-4x) > 0 when x < 1 and (4-4x)<0 when x>1

So the derivative is positive...

(The entire section contains 265 words.)

Unlock This Answer Now




check Approved by eNotes Editorial