Please I need help with this problem!!!!

Question

The Fresnel function, which has applications in optics and highway design, among other areas, is defined as as an integral (accumulation function): .

Determine the -coordinate(s) of the local maximum (maxima) on .

(List all of these values in increasing order. If any blanks are unused, type N in the corresponding blank.)

=

=

=

=

=

=

Answer 1

Using the Fundamental Theorem of Calculus, S'(x)= sin(πx²/2)

S'(x) = 0 when πx²/2 = kπ, where k = 0, 1, -1, 2, -2, ...

So, x² = 2k

x= 0, ±√2 ±2 ±√6, ±√8

Check each one to see if it's a local max.