Answer the questions

Question

f(x) = e(^-3.5x^2)

f) Use the interval notation to indicate where f(x) is concave up

Concave up :

g) use interval notation to indicate where f(x) is concave down

concave down:

List the x values of all the inflection points of f. If there are no inflection points

x= values of inflection points

Answer 1

We need to compute the second derivative and look for those x values that make it 0 (aka, critical points)

y'' = 7(7x^2 - 1) e^{-3.5x^2}

So, x = ±√1/7 are two critical points. Concavity sign is determined by looking at the sign chart, which says concavity is positive for x<-√1/7 or x>√1/7; negative, otherwise