(a) If G(x) = x^2 − 3x + 3, find G'(a) and use it to find equations of the tangent lines to the curve y = x^2 − 3x + 3 at the points (0, 3) and (4, 7).

Answer 1

using our power rule the derivative is g'(a)= 2a - 3. so g'(0)=-3 and g'(4)= 5.

Now use the point slope form, with g' being the slope.

y-3= -3(x-0) and y-7=5(x-4)