Find an equation of a line that is tangent to the graph of f and parallel to the given line.

Question

Function: f(x) = x³

Line: 3x - y + 8 = 0

y= ? (smaller y-intercept)

y= ? (large y-intercept)

Answer 1

Given line first convert to slope-intercept form.

3x - y + 8 = 0 add y on both sides

3x+8=y or y=3x+8 and if tangent line is parallel to this line then the tangent line should have the same slope. so then find the derivative of the function. x^3->3x^2 then 3x^2=3-> x^2=3/3->x^2=1->sqrt(x^2)=sqrt(1)->x=1 then plug in 1 into the derivative. 3(1)^2=9 then put these new number into point-slope form y-9=3(x-1)--------------->y-9=3x-3 then add 9on both sides y=3x+6 so this is the equation that is parallel to y=3x+8 as for the larger y-intercept we can find it by doing this y=3(0)+8->y=8 is the larger y-intercept and y=3(0)+6->y=6 is the smaller y-intercept. I hope this helped you.