Will somebody please walk me through problem 1C-4d in problem set 1? I have to find the equation of the tangent line for the function f(x)=1/sqrt(x) at x=a.

I have the derivative: -(1/2)a^-3/2
No problem with that.

So, next step is to plug it into y-y1 = m(x-x1), right? So that gives me

y-x^(-1/2) = -(1/2)a^-3/2 (x-a)

or

y = -(1/2)a^-3/2 (x-a) + a^-1/2

If this is correct so far, then that should be the equation of the tangent line. But I can't figure out how to simplify it to the answer given in the solutions:

y = -xa^-3/2 + (3/2)a^-1/2

Can anyone help me out?

Question

Will somebody please walk me through problem 1C-4d in problem set 1? I have to find the equation of the tangent line for the function f(x)=1/sqrt(x) at x=a.

I have the derivative: -(1/2)a^-3/2
No problem with that.

So, next step is to plug it into y-y1 = m(x-x1), right? So that gives me

y-x^(-1/2) = -(1/2)a^-3/2 (x-a)

or

y = -(1/2)a^-3/2 (x-a) + a^-1/2

If this is correct so far, then that should be the equation of the tangent line. But I can't figure out how to simplify it to the answer given in the solutions:

y = -xa^-3/2 + (3/2)a^-1/2

Can anyone help me out?

anonymous · Answer

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