Originally posted by fearlessleader
good.🙂
but what the hell dose that mean?😕
you don't know how to differentiate??!
what are they teaching young people these days?!
finding derivatives is the first thing one learns in calculus.
suppose your function is y = 4*x^3 -3*x^2 + x - cos x, and the interval is [-2, 5].
first, find the derivative. the derivative of x^n is n*x^(n-1) for all real
n, and the derivative of cos x is -sin x. thus, we get: y' = 12*x^2 - 6*x + 1 + sin x.
set y' equal to zero since maxima and minima of a function only occur at those points.
the polynomial has no real roots, but sin x is zero at x=0 +
n*pi (here,
n is an integer). unfortunately, there is no place where the derivative is zero so you have no max or min. (sometimes it works like that.)
now we check the boundaries: x=-2 and x=5. for minus two, we get -46 - cos (-2) (which is just cos 2), and for 5, it's 430 - cos 5.
by this reasoning, you only have a min at -2 and a max at 5. (if the interval had been the entire real number set, there would have been
no max or min since it goes large negative for large negative
x and large positive for large positive
x but the cosine would cause what are called
inflection points to appear infinitely often (the graph will "wiggle" at those points, integral multiples of pi).
does it make sense now?