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1.) using the wave speed formula for an electromagnetic wave, c=fλ, (c=3.00x10^8 m/s)

f=c/λ where c=the speed of an electromagnetic wave.

f=(3.00x10^8)/(560x10^-9)= 5.36x10^14 Hz

(1.) (a.) f’(x)=3x^2+6x-2

(b.) x=6 gradient=142

(c.) since f’(x)>0 at x=6, the function is increasing.

In order to prove that one real root of an equation is situated in a certain interval, we calculate the value of the function at the ends of the given interval. In the given case, f(-2) = (-2)^3 - 3*(-2) ...

completing the square: (x+2)^2-9 finding the roots: (x+2)^2=9 x+2=+/-3 at y= 0, x= -5 or 1

dy/dx=12x^2+6 d^2y/dx^2=24x