Question

if f(t)=sqrt(4t+1) find f''(2)

I got the first derivative to be: 1/2(4t-1)^-1/2 * 4t^3

and i'm trying to figure out if i need the product rule again to find the second derivative

-1t^3(4t-1)^-3/2 * 4t^3

The answer if -4/27 and I'm not sure how to get that if I'm doing the second derivative wrong.

Answer 1

I haven't got a clue how you came up with that first derivative.

f(x) = (4t+1)^(1/2)
f ' (x) = (1/2)(4t+1)^(-1/2) (4)
= 2(4t+1)^(-1/2)

f '' (x) = -1(4t+1)^(-3/2) (4)
= -4(4t+1)^(-3/2)
or
= -4/(√(4t+1)^3 )
f '' (2) = -4/√9^3
= -4/27