Question

Consider the function f(x)=x^2e^(9x). f(x) has two inflection points at x=C & x=D with C≤D.
Find these points.

Answer 1

solve f"(x) = 0

f'(x) = 2x*e^(9x) + 9e^(9x)*x^2 = e^(x)*x*(2 + 9x)

f"(x) = (e^x*x + e^x)(2 + 9x) + 9e^x*x = e^x[(x + 1)(2 + 9x) + 9x] = 0

so (x + 1)(9x + 2) + 9x = 0

so 9x^2 + 20x + 2 = 0

Answer 2

uhhh...oops...made an error

Answer 3

f'(x) = e^(9x)*x*(2 + 9x)

so f"(x) = (9*e^(9x)*x + e^(9x))(9x + 2) + 9xe^(9x)

= e^(9x)[(9x + 1)(9x + 2) + 9x] = 0

(9x + 1)(9x + 2) + 9x = 0

so 81x^2 + 36x + 2 = 0

Answer 4

yea i got the same answer x=-2/9 and x=i had gotten -1 too bu ti see where i went wrong

thanks for the fix

Answer 5

solutions:

- sqrt(2)/9 - 2/9
sqrt(2)/9 - 2/9