The displacement (in meters) of a particle moving in a straight line is given bys=t²7t+19,wheretis measured in seconds.

(a) Find the average velocity over each time interval.

(i)[3, 4]

m/s

(ii)[3.5, 4]

m/s

(iii)[4, 5]

m/s

(iv)[4, 4.5]

m/s

(b) Find the instantaneous velocity whent= 4.

m/S

c) a) IfG(x) =x²5x+5,

findG'(a) and use it to find equations of the tangent lines to the curvey=x²5x+5

at the points(0,5)

and(6,11).

y₂(x)

=

(passing through (6,11))