higher derivatives q (1 Viewer)

[blacktown_]

would someone very lovely answer this questions for me and show the working out?

find the exact value of f''(2) if f'(x) = x times by the square root of (3x-4)

muchly appreciated! please and thankyou

 

[blacktown_]

btw its find the exact value of f''(2) if f(x) = x times by the square root of (3x-4)

 

[4025808]

btw its find the exact value of f''(2) if f(x) = x times by the square root of (3x-4)

f(x) = x*sqrt(3x-4)

to get f'(x), differentiate with respect to x by using the product rule.

to get f''(x), differentiate again with respect to x, by using the product rule or w/e

then sub x = 2 into f''(x)

 

[P.T.F.E]

F(X) = x . (3x -4)^1/2
F'(X) = (3x - 4)^1/2 + 1.5(3x - 4)^-1/2
F''(X)= 1.5(3x - 4)^-1/2 - 2.25 ( 3x - 4) ^-3/2
F"(2) = 1.5 * (1/sqrt 2) - 2.25 * (1/sqrt. 8)
= - sqrt 28.125


I THINK... HOPE IT HELPS