find an equations of both lines that are tangent to the curve y=x^3-3x-3 and are parallel to the line 3x -y=15

Question

Please help me

Answer 1

The slope of the lines will be the same as the one given:  since it's written in standard form, negate the x coefficient (-3) then divide by the y coefficient and the math operator in front (-1).  Slope = -3/-1 = 3.  The tangent lines will both have the form y = 3x + b.

Now find the derivative of the cubic function to obtain a function that gives the slope of the cubic function as a function of x.  f'(x) = 3x² - 3.  Now set this function equal to 3 and solve for x.  3x² - 3 = 3 --> x = +/- √2.  Now substitute these values into the cubic equation and find the corresponding values of y.  Then find the values of b in the tangent lines by substituting the x and y pairs into the y = 3x + b equation and solve for b.