Can anyone help evaluate f(x)=(2x+4)/sqrtx
f(0.5)
f'(0.5)
f(0.5)
f'(0.5)
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To do the first part, you have to make x = 0.5, and substitute this into your equation to get:
f(x=0.5) = (2*(0.5)+4)/sqrt(0.5) = 5*2/sqrt(2) = 10/sqrt(2) = 5*sqrt(2)
For the second part, you have to differentiate. So rewrite f(x) as:
f(x) = 2*x^(0.5) + 4*x^(-0.5)
Then differentiate:
f'(x) = x^(-0.5) - 2*x^(-1.5)
Rearrange if you like:
f'(x) = (1 - 2/x)/(sqrt (x))
Then subst. in x=0.5
f'(x=0.5) = (1 - 2/0.5)/sqrt(0.5) = -3/sqrt(0.5) = -6/sqrt(2) = -3*sqrt(2)
And you're done! :)
f(x=0.5) = (2*(0.5)+4)/sqrt(0.5) = 5*2/sqrt(2) = 10/sqrt(2) = 5*sqrt(2)
For the second part, you have to differentiate. So rewrite f(x) as:
f(x) = 2*x^(0.5) + 4*x^(-0.5)
Then differentiate:
f'(x) = x^(-0.5) - 2*x^(-1.5)
Rearrange if you like:
f'(x) = (1 - 2/x)/(sqrt (x))
Then subst. in x=0.5
f'(x=0.5) = (1 - 2/0.5)/sqrt(0.5) = -3/sqrt(0.5) = -6/sqrt(2) = -3*sqrt(2)
And you're done! :)