SOLUTION: Please help! Find the equation of the tangent to the curve y=(x − 2)√(x^2+9) at x=4

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Question 972113: Please help!
Find the equation of the tangent to the curve y=(x − 2)√(x^2+9) at x=4
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Take the first derivative:
(x-2) (1/2)*(x2+9)^(-1/2)*2x + (x^2+9)^1/2 First * derivative of second + second*derivative of first
(1/2)*2x=x
(x-2){(x^2+9)^(-1/2)} + (x^2+9)^(1/2)
x=4
2*25(-1/2) + 25^(1/2)
(2/5) + 5= 27/5
Now find function at x=4
2*sqrt(25)=10
point slope formula with slope 27/5 and point (4,10)
y-10= (27/5)(x-4)
y-10=(27/5)*x - (108/5)
y= (27/5) x -58/5