Maths problems (1 Viewer)

[Real Madrid]

deriving really annoying maths problem

Find the exact value of f"(2) is f(x)= x(3x-4)^(1/2)

 

[bored of sc]

Re: deriving really annoying maths problem

Find the exact value of f"(2) is f(x)= x(3x-4)^(1/2)

f'(x) = (3x-4)^1/2 + 3*1/2*x(3x-4)^-1/2 ----- using product rule and function of a function rule
= (3x-4)^-1/2(3x-4 + 3x/2) ---- factorised out (3x-4)^-1/2
= (9x-8)/2(3x-4)^1/2 ---- cleaned up to form fraction with positive powers

f''(x) = [2(3x-4)^1/2*9 - (9x-8)(3x-4)^-1/2*3] / [4(3x-4)^1/2]² ----- quotient rule
= {3(3x-4)^-1/2[6(3x-4)-(9x-8)]}/(12x-6) ----- factorised 3(3x-4)^-1/2 and expanded bottom line
= [3(3x-4)^-1/2(9x-16)] / (12x-6) ---- expanded inside brackets
= [3(9x-16)] / [3(3x-4)^1/2(4x-2)] ----- moved negative power to bottom line and factorised 3 out
= (9x-16) / [2(3x-4)^1/2(2x-1) ----- cancelled and factorised 2 in denominator
f''(2) = [9(2)-16] / {2[3(2)-4]^1/2[2(2)-1] ---- sub in x = 2
= 2/[2*3*(2)^1/2 ----- expand brackets
= 1/[3(2)^1/2] ---- cancel 2's
= (2)^1/2/6 ---- rationalise denominator

Is that correct?

 

[Real Madrid]

Re: deriving really annoying maths problem

answer

f''(2)=

3
_________
4(2)^1/2

which equals

3(2)^1/2
_________
8

 

[Real Madrid]

Re: deriving really annoying maths problem

thats from the textbook thuogh. I got the same first derivaitve as you, but my answers weird on the 2nd derivative

 

[bored of sc]

Re: deriving really annoying maths problem

Damn.

 

[alex.leon]

Re: deriving really annoying maths problem

It's actually quite simple.



x= heffalump

 

[shaon0]

Re: deriving really annoying maths problem

Find the exact value of f"(2) is f(x)= x(3x-4)^(1/2)

I can't get all my working out as i'm busy at the moment but:

f(x)=x.sqrt(3x-4)
Using product rule
f'(x)=3x/2sqrt(3x-4) + sqrt(3x-4)
Use product rule again and then chain rule you'll get:
f"(x)=[3(9x-16)]/[4(3x-4)^3/2]
Let x=2.
f"(2)=6/[4(2)^3/2]