Question

36. [-/2 Points) DETAILS LARCALC10 2.1.035. Find an equation of a line that is tangent to the graph off and parallel to the given line. Function Line 3x -y +9 - 0 x) = x Y (smaller y Intercept) y = (larger y-Intercept)

Answer 1

* and Given function be o f(x) = x3 -O). line be: 3x-y+9=0 we have from (2): y = 3249 (3) (2) now the slope of the line (3) be: 3. The slope of the parallel line therefore will be: 3. we will be looking for the value of a when the derivative of f(a) equals 3. frow f'(x) = a (x3) - 32² Thus: we have! 3a²=3 Or, 221 x=+1 OY then when when a=1 y = = (2)3 = a į x==1 then y =6103 =24 Therefore the equation of tangent line at (-1,-1) bei y-(-1) =3(2-(-)) or, ytl -3x+3 or y = 3x+ 2 The equation of tansent line at (2, 1) be: y-1 = 3 (x-2) or y 32 - 2 y=134-2 32-2 (smaller y-intercept) ya 32+2] Clarger y-intercept)