Posted by **jon** on Tuesday, January 31, 2012 at 8:17pm.

Find the equation of the tangent line to the curve y=sqrt(x) at x = c. Put the answer in slope intercept form y=mx+b. Use the definition of the slope of the tangent with no short cuts.

- calculus -
**Reiny**, Tuesday, January 31, 2012 at 9:07pm
so the point of contact is (c, √c)

y = √x = x^(1/2)

dy/dx = (1/2)x^(-1/2)

at our point

dy/dx = (1/2)c^(-1/2) = 1/(2√c) = slope = m

y = (1/(2√c) x + b

at(c, √c)

√c = (1/(2√c)(c) + b

times 2√c

2c = c + 2√c b

c = 2√c b

b = c/√c

y = (1/(2√c)) x + c/√c

check my arithmetic

You could rationalize the denominator if you had to.

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