# Let #y = f(x)# be a twice-differentiable function such that #f(1) = 2# and . What is the value of #(d^2y)/(dx^2)# at # x = 1#?

##### 2 Answers

Feb 18, 2017

#(d^2y)/(dx^2) = 28# when#x=1#

#### Explanation:

Let

We have:

#dy/dx = y^2+3#

We know that

#y=2 => dy/dx = 2^2+3=7#

Differentiating the above equation (implicitly) wrt

#(d^2y)/(dx^2) = 2ydy/dx #

And so when

#(d^2y)/(dx^2) = 2(2)(7) = 28#

Feb 18, 2017

#### Explanation:

After two derivations, the terms like