Consider the function below. (Give your answers correct to two decimal places) a

Question

Consider the function below. (Give your answers correct to two decimal places)

a) Use calculus to find the interval of increase. (____, ____)

b) Use calculus to find the intervals of decrease. (Enter the interval that contains smaller numbers first.)

(____, ____) U (____, ____) U (____, ____)

c) Use calculus to find the intervals where the function is concave up. (Enter the interval that contains smaller numbers first.)

(____, ____) U (____, ____)

d) Use calculus to find the intervals where the function is concave down. (Enter the interval that contains smaller numbers first.)

(____, ____) U (____, ____)

Consider the function below. f(x) = 1+1/x+9/x2+1/x3 Use calculus to find the interval of increase. Use calculus to find the intervals of decrease. Use calculus to find the intervals where the function is concave up. Use calculus to find the intervals where the function is concave down.

Explanation / Answer

f'(x)=(-1/x^2)+(-18/x^3)+(-3/x^4)

=-(x^2+18*x+3)/x^4

so for interval of increase,

f'(x)>0

x^2+18*x+3<0

x=-0.168 or x=-17.83

so interval is (-17.83,-0.168)

b)

interval of decrease=(-inifinity,-17.83) U (-17.83,-0.168)

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