# Thread: Calc anti derivative

1. ## Calc anti derivative

Consider the function f(x) = 4 sin(x2) on the interval 0 ≤ x ≤ 3.

(a) Find the exact value in the given interval where an antiderivative, F, reaches its maximum.
x =

(b) If F(1) = 6, estimate the maximum value attained by F.
y

2. Originally Posted by bluejewballs
Consider the function f(x) = 4 sin(x2) on the interval 0 ≤ x ≤ 3.

(a) Find the exact value in the given interval where an antiderivative, F, reaches its maximum.
x =

(b) If F(1) = 6, estimate the maximum value attained by F.
y

Do you mean $4\sin{2x}$ or $4\sin({x^2})$

3. x^2

4. Originally Posted by bluejewballs
Consider the function f(x) = 4 sin(x2) on the interval 0 ≤ x ≤ 3.

(a) Find the exact value in the given interval where an antiderivative, F, reaches its maximum.
x =

(b) If F(1) = 6, estimate the maximum value attained by F.
y
To find maxima, we differentiate and set the function to zero. Then we evaluate the value of x for which this happens. Do the same thing... So what is the derivative of the antiderivative of f(x)?(with carefully defined limits)