Calculus quiz

[Ohkrana]

Something a little different I guess. I'll Try a calculus maths quiz and see if this takes off. Same rules apply; he who answers correct claims the right to ask the next question.

I'll go with something straight forward, not sure how much calculus, people have under their newtonian belt here!

For X in the region [-4,2]

F(x) = (x^2 - 3)*e^x

What I'm looking for from you maths buffs:

The First derivative F'(x) ...
[edit : thanks for pointing out my grammatic error ]

Where Points of Extrema (maximums or minimums) occur...

Whether the points of Extrema are maxiums or minimums..
*hint you'll need F"(x)*

 

[ainwood]

Originally posted by Ohkrana
What I'm looking for from you maths buffs:

The First derivative of F'(x) ...

*hint you'll need F"(x)*

Of course we will. The first derivitive of F'(x) is F''(x).

 

[omichyron]

I'm taking calculus next year, so I am not yet equipped to answer this.

 

[allhailIndia]

the equation is y=(x^2 - 3)e^x

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

Equating it to 0 we get

x^2-2x+3=0.

The roots of this equation are 3,-1.

F"(x)=e^x(2x-x^2-3+2x-1)
replacing the value of x to this we get

F''(x)=e^3(-1)
=>F"(x)<0
=>3 is the point of maxima and hence -1 is the point of minima.

Is it right??

 

[Ohkrana]

Ah, so close my friend, good show though. Check your working, your mistake is in the second line of your post; F'(x).

 

[Rain]

should be e^x (2x+(x^2 - 3)) or e^x(x^2+2x-3) giving

e^x{(x+3)(x-1)}