Question #e9697

3 Answers
Jul 20, 2017

0

Explanation:

f(x) = 6sqrt4 + x = 12+x

f'(x) = 1

f''(x) = 0

0

Explanation:

Some basics
1. Derivative of constant is zero
2. Derivartive of '(x^n)' is nx^(n-1)
So solving,
d(6*4^(1/2)+x)/dx
so,
=1
Now diffrentiation of 1 is zero

Jul 22, 2017

y=6sqrt(4+x) .rArr (d^2y)/dx^2=(-3/2)(x+4)^(-3/2).

Explanation:

Let, y=6sqrt(4+x).

:. dy/dx=d/dx{6(x+4)^(1/2)},

=6d/dx{(x+4)^(1/2)}.

Now, we know that, d/dx{x^n}=nx^(n-1).Hence,

dy/dx=6*1/2(x+4)^(1/2-1)d/dx{(x+4)},......."[The Chain Rule],"

rArr dy/dx=3(x+4)^(-1/2).

Hence, (d^2y)/dx^2=d/dx{dy/dx},............"[Definition],"

=d/dx{3(x+4)^(-1/2)},

=3d/dx{(x+4)^(-1/2)},

=3{(-1/2)(x+4)^(-1/2-1)}d/dx(x+4),

rArr (d^2y)/dx^2=(-3/2)(x+4)^(-3/2).