Find a general expression for the slope of a tangent line to the indicated curve. Then find the slopes for the given values of x. Sketch the curves and tangent lines.

y=x2+3.5x+3; x=2, x=2.5

Find the average rate of change of y with respect to x from P to Q. Then compare this with the instantaneous rate of change of y with respect to x at P by finding mtan at P.

y=3x2+2; P(4,50), Q(4.1,52.43)

Calculate the instantaneous velocity for the indicated value of time(in s) of an object for which the displacement(in ft) is given by the indicated function. Calculate values of the average velocity for the given values of t and note the apparent limit as the time interval approaches zero.

s=4t+3; when t=5; use values of t of 4.0, 4.5, 4.9, 4.99,