Question

Produce graphs of f that reveal all the important aspects of the curve. Then use calculus to find the following. (Enter your answers using interval notation. Round your answers to three decimal places.)

f(x) = e^x − 0.196x⁴

Find the inflection points of the function.

(x, y)	=	(smallest value)
(x, y)	=
(x, y)	=	(largest x-value)

Find the interval(s) where the function is concave up.

Find the interval(s) where the function is concave down.

Answer 1

e 0.19624 Given f(x) = at f00)=0 Inflection points occors f(x) = d da ex - 0.196 (423) -e da x=n-an- - ex 0.784 03 F"CO) d d da [ f'(a)] dy[ed_0078483 ed 0.784 (302) ed_ 2.352x² >> ea 2-35232 by using calculator, (x+0.506) (2-1.171)=0 x = -0.506 inflection points 8x = 1.17 occox at a = -0.506 1.171 when x= -0.506 - y = f(-0.506) 0.59005 = 0-590

x = 1.171 - 2.8586 2.859 = (1.17) inflection points are (-0.506, 0.590 ) /smallest se value I female (1.171, 2.859 ) loogest F" (Do Concave up F" (o co Concave down t`value The available intervals (-0, – 0.506), (0.506, 1.171) (1.171, 0) f" (-1 = el- 2.352 CAD In (-∞, -0.506) To (down) In (-0.506, 1-171) = » f(1) = e = 2.352 (18² So Cop) In (1.17), x) = f'(2) = ² - 2.352 (2) ² <o (down) f(x) is concare up on (-0.506, 1.171) F(x) as concave down on (-0, -0.506 € (1.171,00