Tangent Lines-Calculus

posted by .

a line is tangent to the curve y= (x^2 + 3)/ (x+3)^1/2 at the point where x=1.

write the equation of this line

i get y= 3x-1 yet it's wrong. please explain thank you

• Tangent Lines-Calculus -

y=(x^2+3) / (x+3)½
y(1) = 4/2 = 2

y' = 3(x^2+4x-1) / 2(x+3)3/2
y'(1) = 3(4)/2*8 = 3/4

so, now you have a point (1,2) and a slope (3/4)

y-2 = 3/4 (x-1)

Similar Questions

1. Calculus

Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean?
2. Calculus

Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean?
3. Calculus

Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean?
4. Calculus

Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean?
5. calculus

Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show that dy/dx= (4x-2xy)/(x^2+y^2+1) b. Write an equation of each horizontal tangent line to the curve. c. The line through the origin with slope -1 is tangent to the curve …
6. Calculus

Please help this is due tomorrow and I don't know how to Ive missed a lot of school sick Consider the curve given by the equation x^3+3xy^2+y^3=1 a.Find dy/dx b. Write an equation for the tangent line to the curve when x = 0. c. Write …
7. Tangent Lines (2)-Calculus

find an equation of the line tangent to y= sqrt(25-x^2) at the point (3,4) i got y= x/8 + 29/8 this is wrong. but im not sure why. can you explain thank you
8. Math

In this problem we consider drawing some straight lines which form a nice pattern. Consider joining the point (0.1,0) to the point (0,0.9) by a line segment; then joining (0.2,0) to (0,0.8) by a line segment; and so on. In general, …
9. Calculus AB

Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive?