(a) If G(x) = x2 − 5x + 5, find G'(a) and use it to find equations of the tangent lines to the curve y = x2 − 5x + 5 at the points (0, 5) and (4, 1)

Question

(a) If G(x) = x² − 5x + 5, find G'(a) and use it to find equations of the tangent lines to the curve y = x² − 5x + 5 at the points (0, 5) and (4, 1)

G'(a)=_______

y₁(x)=_______ (passing through (0, 5))

y₂(x)=_______ (passing through (4, 1))

Answer 1

Use the power rule to get the derivative. G'(a) thus equals 2a-5. This is the slope of your tangent, or m. Your equation of a line passing through a point is y-b = m(x-a) where (a, b) is your point. Now plug in G'(a) for m, plug in your specific values of a and b, and solve!