for what values of a and b will the parabola y =x^2 + ax + b be tangent to the curve y = x^3 at point (1,1)?
First you will want to find the derivative of: . Using the power rule, Now plug in the 1 to find the slope of the curve at x = 1. . Now you will want to find the derivative of the equation and set that equal to the derivative of . So and
Substituting in the 1:
Now that you have the a-value, you will want to solve for b. Set to get the b.
Finally, the equation of the parabola tangent to the cubic is: