Question

(a) if g(x) = x2 − 3x + 3, find g'(a) and use it to find equations of the tangent lines to the curve y = x2 − 3x + 3 at the points (0, 3) and (2, 1).

Answer 1

Using the power rule, $g'(a) = 2x-3$.

At x = 0, $g'(0)=-3$. Therefore, the slope of the tangent line is -3. In point-slope form, the equation of the line tangent to the curve at (0,3) is $y-3=-3(x-0)$. 

At x = 2, $g'(2)=1$. Therefore, the slope of the tangent line is 1. In point-slope form, the equation of the line tangent to the curve at (2,1) is $y-1=1(x-2)$.