3. Find the equation of the tangent line to the curve y = _ at x =3 X Slope: Need the slope at x=3. So, we need to calculate the derivative: f' (x ) - lim J ( x+h) -f(x) h-0 lim &th & , need to get a common denominator to combine the fractions in h h-0 h the numerator... 2 . (x) _ 2. (xth) 2X 2(x4/) 24-28-2/ lim ah (x) & (xth) - lim (xth) x(xth) X(XAN) -2h -2 -2 -lim- - lim lim 2 h-0 h h 1-0 h ho h( x) ( x+h) 10 x(x+h) x(x+0) x 2 So, f' ( X ) - - 2 The slope at x=3 can be found by evaluating the derivative at x=3. f' (3) -_2 N (3) 9 So the slope, m, is -2/9. Point: When x = 3, y = f(3) = 2/3. So, (X1,y1) = (3, 2/3) Point-Slope form.. 2_ IN 2 4 y - (X -3) - WIN WIN y X+ 3 9 9