1.with the function: f(x) = x^2e^-3x(adsbygoogle = window.adsbygoogle || []).push({});

a)find f'(x) and f''(x)

b)find the critical points of f(x)

c)use the derivative to determine where f(x) is increasing and decreasing.

d)use the second derivative to determine where f(x) is concave up and concave down. Identify any points of inflection.

I got the first and second derivative, I just want to make sure I took the derivative correctly.

f'(x)= 2x(e^-3x) - (3x^2)(e^-3x)

f''(x)= 2(e^-3x) + (9x^2)(e^-3x)

Then I set the first derivative equal to zero in order to find the critical points.

getting x= 0 and x= 2/3

I want to make sure I did a and b correctly, then I need some help with c and d.

----------------------------

2. For the function y= axe^-bx^2 use calculus to find exact values of a and b so that the function has a maximum at (2,1).

I tried taking the derivative and then plugging in the x and y values, but I'm having trouble finding a and b.

y'= a(e^-bx^2) - 2bxax(e^-bx^2) then plugging in (2,1)

1= a(e^-b(2)^2) - 2b(2)a(2)(e^-b(2)^2)

I'm lost after that part.

-------------------------------------------

3. Use calculus to find the best bounds for f(t)= tsqrt(4-t^2) for -1 =< t =< 2 (-1 less than or equal to t, and t less than or equal to 2.

I believe you take the derivative and then set it equal to zero to get the critical points. After that, I need some help to get the bounds.

thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Find derivatives and bounds of x^2 e^(-3x)

**Physics Forums | Science Articles, Homework Help, Discussion**