Calculus
posted by ashley
Can someone check my work on this problem? I'm studying for the AP test and I would really appreciate any help.
Let f(x) = the definite integral from [2,(x^23x)] of e^(t^2) dt
At what value of x is f(x) a minimum?
a. For no value of x
b. 1/2
c. 3/2
d. 2
e. 3
The answer I got was 3/2. Here's my process:
h'(x)=e^(x^23x)^2dv/dxe^(2^2)du/dx
=(2x3)e^(x^23x)^20*e^(2^2)
(2x3)e^(x^23x)^2=0 to find the critical point which would be at 3/2.
Thank you!!

Steve
your logic and your answer are correct.
Respond to this Question
Similar Questions

Calculus  Derivatives
The approximation to a definite integral using n=10 is 2.346; the exact value is 4.0. If the approximation was found using each of the following rules, use the same rule to estimate the integral with n=30. A) Left Rule B) Trapezoid … 
Calculus
We are doing problems with the product and quotient rules, but I'm not sure if I'm doing them correctly. If someone could check my answer I would really appreciate it. The original problem was y = (2x1)^5 * (4x+1)^1 and I got the … 
calculus
There are four integrals: 1) definite integral x/(1+x^4)dx b/w 0_infinity 2) definite integral (x^2)/(1+x^4)dx b/w 0_infinity 3) definite integral (x^3)/(1+x^4)dx b/w 0_infinity 4) definite integral (x^4)/(1+x^4)dx b/w 0_infinity Which … 
calculus
There are four integrals: 1) definite integral x/(1+x^4)dx b/w 0_infinity 2) definite integral (x^2)/(1+x^4)dx b/w 0_infinity 3) definite integral (x^3)/(1+x^4)dx b/w 0_infinity 4) definite integral (x^4)/(1+x^4)dx b/w 0_infinity Which … 
Calculus
Can someone explain to me how to do these? 
Calculus
"Leave the answer as a definite integral, but indicate how it could by evaluated by using the fundamental theorem of calculus." I solved the problem to a definite integral. Proceeding via the fundamental theorem, would involve finding … 
Calculus (urgent help)
consider the function f that is continuous on the interval [5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral: … 
calculus
consider the function f that is continuous on the interval [5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral: … 
calculus (please with steps and explanations)
consider the function f that is continuous on the interval [5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral: … 
Math (Definite Integrals)
Sketch the region given by the definite integral. Use geometric shapes and formulas to evaluate the integral (a > 0, r > 0). r ∫ sqrt(r^2  x^2) dx r While I recognize that this looks similar to a circle function, I'm not …