Question

For the function f(x)=3cos(2x),what is the first point where it is increasing the fastest?
Also please tell me how you know or derived that!
Thank you!!! Please answer ASAP

Answer 1

the slope is given by the derivative

f(x) is increasing fastest where the slope is steepest. That is, the derivative has a maximum.

Take a look at the graphs of f and f' and you will see that for this problem, f is increasing fastest when x = 3π/4

http://www.wolframalpha.com/input/?i=plot+y%3D3cos2x,+y%3D-6sin2x

Answer 2

I have no idea what a derivative is. Im in precalculus or advamced functions. That isna calculus topic. Is there any other way to explain it? Thank you

Answer 3

i know you guys are busy but please

Answer 4

In that case, just look at the graph. It is clear that cos(x) is steepest where it crosses the x-axis.

Without calculus, I can't think of an analytical test to prove where the slope is steepest. Are there any similar problems in your text?

Answer 5

not at all but it is on the practice exam he provided.
But your answer makes sense thank you!