What is the second derivative of #f(x)= 2x^3- sqrt(4x-5)#?

Answer 1

#12x + 4/(4x - 5 )^(3/2) #

to obtain the second derivative means differentiating the function to obtain f'(x) and then differentiating f'(x) to obtain f''(x).

rewriting f(x) as # f(x) = 2x^3 - (4x - 5 )^(1/2) #

applying the chain rule :

#f'(x) = 6x^2 - 1/2 (4x - 5 )^(-1/2).d/dx(4x - 5 ) #

# f'(x) = 6x^2 - 1/2 (4x - 5 ).4 = 6x^2 - 2(4x - 5 )^(-1/2) #

#f''(x) = 12x + (4x - 5 )^(-3/2).d/dx(4x - 5 ) #

#rArr f''(x) = 12x + (4x - 5 )^(-3/2).4 = 12x + 4/(4x - 5 )^(3/2) #

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Answer 2

Christopher Allers

The second derivative of ( f(x) = 2x^3 - \sqrt{4x - 5} ) is:

[ f''(x) = 12x - \frac{2}{\sqrt{4x - 5}} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.