Hello, I need help those calculus question. Would you please help me to solve those...

Questions I. Given 9(1) = 3h: a. Determine whether the Extreme Value Theorem is applicable over [0,2]. If not, find an Interval over which the Extreme Value Theorem is applicable. Justify your answer. [10 points] b. If the EVT is applicable, find the extreme values of 9' over [0.2]. [10 points] 2. Evaluate the specified derivatives [9 points each]: a. 01 arctanx 7 8 arccscx 7 arcsin 2x) b. gnu-=1\" + 2 sin(e')) c. (7Jm4Iny + 9) d. ditch-10:2 + 1)) when t = 2. 3. Given the curve defined by x2 + 3xy + y3 = 29, a. Find dy/dx [8 points] b. Find the slope of the curve at the point (1.4) [4 points] -2r'(r+3) _ s 4- SUPPOSE f0!) = riff?!) = w: and f"(x) = -2x(r?+sr+ 12) [rd-2)! ' a. Determine the intervals on which f is Increasing, [8 points] b. Determine the intervals on which f is decreasing, [8 points] c. Find any critical numbers and determine what occurs at each. [6 points] 2 5. Let h be a differentiable function with domain (6.11). Further, suppose 3 > D on the Intervals (6, 3), (3.0),and (6,8) and :27: