Consider a curve of the form y(t) = at + g, with a local minimum at (3, 12) . (a) Given only (3, 12) tells us that O y(12) = o O y(3) = 12 O y(12) = 3 O 143) = 0 Given that (3, 12) is also a local minimum tells us that O y '(12) = o Oy'(3)=12 Oy'(3)=0 Oy'(12)=3 (b) Find y '(t) = (c) Now find the exact values of a and b that satisfy the conditions in part (a). b=