Question

18. Find the absolute maximum point of the function h(x) = -=-** -x +5x2-1. 19. Set up, but do not solve, the integral to find the area between the x-axis and the function z(x) = x² - 4 on the domain [0, 10).

need help with these two please!

Answer 1

x + 5x², (18) Giken function h(x) = 2 For critical points o hicx)=0 | + (x) = 4 + 5-7 hix) = € - 3x², - 3x² + 10x =-x²3x²10x. h(x) = -x² – 3x²tro x =0 -) X(-42-3x +10) = 0

x=0 (68) - x² – 3x+10=0 x = (-3) 1 J (-37-4-1) (10) (2)(-1) - 31 59 +40 317 = x -2 = – 5,2 x=0, 2 critical values -5 hex) Value at critical points in hola lort - (0)² + 5193², = ~ h (2) = -fast - (23*+ 56032-4 = 7 h65) = -4-574_45 ) +5(+5)=-= 37 * hol= - h(2) = 7 > h(-5) = 371 LAM Absolute maximum | Absolute maximum = 371 at x=-5 = -5 - Absolute point maximum

Criven ZOW= x²_4 on the domain [0, 10] and x-ar 20%) Z(x)=x² 4 ..Area = [o-2(x] dx + ( [z(x) - ol de Area = - f (2²4) dx + $ (224) dx/ X