Compute the derivative function f'(x) algebraically. HINT [See Examples 2 and 3.] f(x ) = x2 + 8 F' ( x ) = Compute the indicated derivative. U(t) = 5.5+2 + 5.5; U'(4) U'(4 ) = Compute the derivative function f'(x) algebraically. HINT [See Examples 2 and 3.] f(x ) = 9x2 + x F ' ( x ) = Compute the derivative function f'(x) algebraically. HINT [See Examples 2 and 3.] f(x) = -6x - 5x2 F ' ( x ) = Compute the indicated derivative. U(t) = 5.5t2 + 5.5; U'(4) U'(4) = Find the equation of the tangent to the graph at the indicated point. F(x ) = x2 - 1; = = 5 Find the equation of the tangent to the graph at the indicated point. f(x) = 2x + 1; = = 7 Velocity If a stone is dropped from a height of 450 feet, its height after & seconds is given by s = 450 - 16t. Find its instantaneous velocity function. v (t ) = Find its velocity at time t = 2. v(2) : ft/sec Daily crude oil production by Pemex, Mexico's national oil company, for 2008-2013 could be approximated by P(t) = 0.017tz - 0.4t + 5.23 million barrels (8 s t = 13), where t is time in years since the start of 2000. Find the derivative function JR. It . HINT [See Example 4.] dt At what rate was oil production changing at the start of 2011 (t = 11)? Daily oil production was decreasing at a rate of million barrels per year. Velocity If a stone is thrown down at 160 feet per second from a height of 980 feet, its height after t seconds is given by s(t) = 980 - 160t - 16t". Find its instantaneous velocity function. v(t ) = Find its velocity at time t = 3. V(3) = ft/sec