Find the gradient of the tangent

[arvins9]

Homework Statement

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

sinx+x$$\leq$$f(x)$$\leq$$8$$\sqrt{x+4}$$-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 $h'(x)= 4(x+ 4)^{-1/2}$ 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 $h'(x)= 4(x+ 4)^{-1/2}$ and h'(0)= 4/2= 2, not -2.

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