Use a graphing utility to find intercepts, relative extrema, points of inection and asymptotes for # 1-4. _ (H2) _(5x2+4x+10) 1"rm(32:4) 2'f(x)_ (5x5) 3. f(x)=(2x2-3)2 14- f(x)=|x36x2+3x+3l 5. An open box is made from a rectangular piece of material by cutting equal squares from each comer and turning up the sides. Find the dimensions of the box with maximum volume if the piece of material is 10 inches by 2 inches. 6. The length of a rectangular yard is measured to be 84 feet and the width to be 36 feet. If the measurements are correct to within 0.25 feet, use differentials to estimate the propagated error in the area of the yard. 7. Find the price per unit p that produces the maximum prot given C = 2500 75x + 0.042:2 and p = 20000.6x2 . Use P = xp-C 8. Find fi/x3dx 9. Find f2csc2(3x)dx . (6x3 5x5) . sink/g) 10.F1nd f7_ax 11.F1r1d dex 12. Find y=f(x) if f"(x)=4x2 , f'(0)=3 ,and f(0)=2. 13. Use a(t) = -32 feet per second squared as the acceleration due to gravity. A ball is thrown vertically upward om the ground with an initial velocity of 50 feet per second. How high will the ball g0? Using the Fundamental Theorem 0f Calculus, nd the area of the regions bounded by 14. y=2 @x, y=0 15. y=8x, x=0, x=6, y=0 16. y = 5x .t= and the x-axis 3 t32 17. Given F(x)= f( )4: nd not) and F13). 18. Find f 2x3(2x" 1)3dx 19. Find f SU'lxl . 20. Find f 2.t,/(5_t~3)i1.i