Question

Find f''(x) for the function f(x) = √(9x - 7).

a) f''(x) = 0
b) f''(x) = 27/(4√(9x - 7)^5)
c) f''(x) = -27/(2√(9x - 7)^5)
d) f''(x) = 27/(2√(9x - 7)^5)

Answer 1

To find the second derivative, we first find the first derivative using the chain rule, and then take the derivative of the first derivative.

Step-by-step explanation:

To find the second derivative, f''(x), of the function f(x) = √(9x - 7), we need to take the derivative of its first derivative, f'(x).

First, we find f'(x) by applying the chain rule: f'(x) = (1/2)(9x - 7)^(-1/2) * 9 = 9/(2√(9x - 7)).

Next, we take the derivative of f'(x) to find f''(x):

f''(x) = d/dx[f'(x)] = d/dx[9/(2√(9x - 7))] = -27/(4√(9x - 7)^3).

Therefore, the correct option is b) f''(x) = 27/(4√(9x - 7)^5).