calculus
posted by jon .
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.

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.
Respond to this Question
Similar Questions

calculus totally confused
find a first degree polynomial function p(1) whose value and slope agree with the value and slope of f at x=c. i think you use taylor series for this f(x)=4/sqrt(x), c=1 i'm totally confused on how to do it. i know you find the derivative … 
12th Grade Calculus
1. a.) Find an equation for the line perpendicular to the tangent curve y=x^3  9x + 5 at the point (3,5) [* for a. the answer that I obtained was y5 = 1/18 (x3) ] b.) What is the smallest slope on the curve? 
Calculus
There are two neighboring points P and Q on the curve f(x)=x^2 (a) Determine m(h), the slope of the straight line PQ (b) The slope, S, of the tangent at P is defined as S=lim h>0 m(h). Find the value of S. (c) Use this value of … 
Calculus 251
The slope of the tangent line to the curve y= 3x^3 at the point (1,3) is:? 
Calculus
the slope of the tangent line to the curve y=(3/x) at the point (6,0.5000) is? 
Calculus
If F(x)=x^3−7x+5, use the limit definition of the derivative to find FŒ(5), then find an equation of the tangent line to the curve y=x^3−7x+5 at the point (5, 95). FŒ(5)= The equation of the tangent line is y = x … 
Calculus
Suppose that y=f(x) = sqrt(2x), x>=0 Find a c > 0 such that the tangent line to the curve y = f(x) at x = c has the same slope as the tangent line to the curve y = f^–1(x) at x = c. You get: c = 1/8 c = 1/2 c = (1/8)^(1/3) … 
Math
Suppose f(x)=5/(x2). f'(5)=5/9. Use this to find the equation of the tangent line to the curve y=5/x2 at the point (5,(5/3)). write your answer in the form y=mx+b where m is the slope and b is the yintercept. The equation of the … 
calculus
Find the slope of the tangent line to the curve (sqrt(4x+y))+(sqrt(3xy)) at the point (3,4) The slope of the tangent line to the curve at the given point is ? 
Calculus AB
Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x1)e^x. For which value of x is the slope of the tangent line to f positive?