Find the gradient of the tangent

[arvins9]

Homework Statement

For every x>-4 where x\in \Re applies

sinx+x\leqf(x)\leq8\sqrt{x+4}-16

Find the gradient of the tangent to the curve of f at x_{0}=0

Please help me I am trying to solve this exercise for more than two hours!
I'm desperate.

 

[nik21bigbang]

i think the functions is g(x) <=f(x)<=h(x) has
slope [g(x) at x=0 ] = 2 and
slope [h(x) at x=0 ] = -2
however i think the function is too many in between so the question is not relevant [ i think].

 

[HallsofIvy]

i think the functions is g(x) <=f(x)<=h(x) has
slope [g(x) at x=0 ] = 2 and
slope [h(x) at x=0 ] = -2

No, h(x)= 8\sqrt{x+ 4}- 16= 8(x+4)^{1/2}- 16
so h&#039;(x)= 4(x+ 4)^{-1/2} and h'(0)= 4/2= 2, not -2.

however i think the function is too many in between so the question is not relevant [ i think].

 

[nik21bigbang]

No, h(x)= 8\sqrt{x+ 4}- 16= 8(x+4)^{1/2}- 16
so h&#039;(x)= 4(x+ 4)^{-1/2} and h'(0)= 4/2= 2, not -2.

i think you should recheck your answer,please see h'(0) = -2