Please answer these 7 questions! Thank you!

\f2. Let f(x) = Vx +1. (a) (10 pts) Find the equation of the tangent line to the graph of y = f(x) at r = 8. (b) (10 pts) Using the linearization of f(x), approximate v9.13. Let f(x) = - 2 4 (If your work is not consistent, you will receive zero on all of the subquestions). (a) (5 pts) Find the domain of f. (b) (5 pts) Find f'(x). (c) (5 pts) Find the critical values of f(I). (d) (5 pts) Find for which a values f is increasing. (Your answer SHOULD be interval(s).) (e) (5 pts) Find for which a values f is decreasing. (Your answer SHOULD be interval(s).)(f) (5 pts) Find the local extreme value(s) of f(x). (g) (5 pts) Find f"(x). (h) (5 pts) Find for which a values f is concave-up. (Your answer SHOULD be interval(s).) (i) (5 pts) Find for which a values f is concave-down. (Your answer SHOULD be interval(s).) 5\f4. {10 pt) Find the absolute maximum and minimum of x) = $23:- 2 on [1,3]. {Note that this is the same function with the function in the previous problem.) 5. {10 pts) Determine whether Mean Value Theorem applies to HI) = :1: +$ on [1,3]. If an, nd the point[a) that are guaranteed to exist by; the theorem. E. {ll} pts} A hotair hallo-on is 171] ft above the ground when a motorcycle passes directly beneath it [traveling in a straight line on a horizontal road} going 40 ft]?r s. If the balloon is rising 1vertically,r at a rate of 13 ftfs, what is the rate of change of the distance between the motorcycle and the balloon ll} seconds later? 7. Consider f(x) = 15 - 3x2 + 6x + 2. (a) (10 pts) Show that f(x) has a root in the interval [-2, 3] without finding any root. (b) (10 pts) Use Newton's method to approximate the root of f(r) in the interval [-2,3]. Let To = 3 and find X1, I2, . . . ; $10