I took the derivative and am trying to find certain values that makes the derivative zero. I found all the parts except the third and I am a little stumped.

Question

I was given a function and I took the derivative which is kcos(bt²)*2bt for which my grading system marked correct.

the question has two other parts where it says t=1 if f'(t)=0; find the exact values for b and (same perameter different part) for k that satisfy these conditions.

I found b to be pi/2

and I thought k would be zero, but that was marked wrong.

I am confused because k beign zero would make everything multiplying zero therefore making the derivative zero. K isn't special like b, so the only value to mak the derivative zero would be 0. I am so confused.

Answer 1

if t = 1, then;  2b* k*cosb = 0

 

the angles b = 90 degrees or pi/2; and 270 degrees or 3*pi/2 are answers for this question. Remember that cosine is zero at 90 and 270 degrees.  

 

The original function would be k*sin(bt).   k represents the amplitude of this sinusoidal function, there is apparently not enough information given to get a definitive value for k, so as it stands, k could take on an infinite amount of different values.