Question

d 4. Use the definition of the derivative to show that dr (3x2 - 4) = 62. You must use the definition of the derivative to receive credit. The height A (in feet) of an object shot into the air from a tall building is given by the function 10) = 510 + 801 – 1662, where t is the time elapsed in seconds. (a) Write a formula for the velocity of the object as a function of time t. ht) (b) What should be the velocity of the object when it reaches Rs highest point? ft/sec When does this occur? (c) What is the maximum height reached by the object? ha At (d) Write a formula for the acceleration of the object as a function of time to ht) - ft/sec

Answer 1

d (3n-u) .62 dr el ele ale d (an) nanal an d (constant) = 6 dn 2-1 6n d d n an (34) hitle 610+ 80t -16+2 velocity h(t) (LU) 80-32t ar at h' (t) At highest 80-32€ ft/se by At highest point velocity is tuo, point acceleration and velocity are [tero occus when y = highest point It occus v2-uz-zas to sonorons 32 80-320 =0 X6 842 It-2.5 sec

4) aculuation or h"(t) d (n't)) dt - 80 -32+) 2-32 acceleration h" (t) = 1-32 ft/see? c) Maximum height SELLE 29 & u2 2x9.8 where his intial verlocity