calculus homework problem?

Question

for f(x)=x^2 + e^(x^2) with endpoints -0.5 f(x) has local min
f(x) has local max
f(x) has global min
f(x) has global max

thanks

for clarity the equation is f(x)=x^2 + e^x^2
e is raising x to the 2nd power

Answer 1

f(x) = x^2 + e^(x^2)
df/dx = 2x + 2x e^(x^2) = 2x[1 + e^(x^2)] = 0

There's a max or min at x=0, and that's the only one because e^(x^2) cannot go negative, i.e., e^(x^2) = -1 will not happen.

For the rest of your problem, evaluate your function at the endpoints.

Answer 2

First find dy/dx [ f'(x) ], that is, derivative of the function f(x).
Then find for which values of x is its value 0 and see if any value is from the given interval.

Next perform second differentiation [ f''(x) ] on the function and substitute the value you just got and check the sign of your answer. If it is negative it is a maxima and if it is positive the point is a minima.

After you have found the required x co-ordinate you just put them in the given equation and find the respective y co-or.

But I can't tell you properly how to differentiate between a local or global maxima / minima.

Answer 3

Invalid question....you have a typo.