Maxima and minima of an equation.

[cobber82]

Someone help me with my math question?


For x < 0 find it terms of b and c, expressions for the x values of the first 2 minima and the first two maxima. State which solutions give the max and min, give reasons for your answers.


The original equation is f(x)=a*cos²(bx)*e^-cx


And question beforehand was to differentiate it.
The answer to this is f'(x) = (-ae^-cx*cos(bx)*(c*cos(bx)+2*b*sin(bx)

 

[cobber82]

Actually, I made a mistake. f'(x) = e^-c*x(-a*c*(cos²(b*x) - 2*a*b*sin(b*x)*cos(b*x)
Woopsies.
Anyway, should I be using the gradient function at all to find the 2 minima and maxima?

 

[Deleted member 4993]

Actually, I made a mistake. f'(x) = e^-c*x[-a*c*cos²(b*x) - 2*a*b*sin(b*x)*cos(b*x)]

Woopsies.
Anyway, should I be using the gradient function at all to find the 2 minima and maxima?

What is the value of f'(x) for extrema (maxima or minima) of f(x)? and

what will be the "sign" of f"(x) for maxima? for minima?