Question

Problem 4. Find the derivative of the faction yan" - VI Problems. Find the derivative of the function y=sin( 2.1) Problem 6. Find the derivative of the function (x) - sinh(x'). Problem 7. Find the limits. Use L'Hospital's Rule where appropriate. (a) lime (b) lim ( sinx Inx) I Problem 8. Sketch the graph of a functionſ that is continuous on [1, 5] and has absolute minimum at 2, absolute maximum at 3, local minimum at 4. Problem 9. Sketch the graph of a function that has a local maximum at 2 and is continuous but not differentiable at 2. Problem 10. Find the critical numbers of the function f(x) = x + x? -. Problem 11. (Extra credit, 10 pts.) Find the absolute maximum and absolute minimum values of f on the given closed interval. f(x)= x - 6x + 5 ; (-3,5).

Answer 1

Problems to f(x)= x²+x²_x f'ca) = 3x +22. put f'(x) = 0 3*2 + 2x = 0 2 (3x+2) = 0 2-O 2 - Critical points. 2- -2

Problem feos = x²6x²+5 ; E3,5] fied absolute maaima and minima Sol fw 3x² _ 128 Put f'(x) = 0 372-122=0 X(32-12) 220 x=4 Now, $(x) 6% -12 when f"(x) co absolute maxima

when x= 4, f''(x) > 0 absolute minima

at 2 Pooblem 9 local maxima (2,01 continous but not differentiable at x = 2 Problem 8 X C) (2,0) 3,0) (4,0)(50)