hello Friends,
I cant solve out this problem.
For the following function, find a point of maxima and point of minima,if these exist:
f(x)=17x^5-14x^3+44
Thanks
Harshal.
Differentiate and classify the zeros of f'(x)=0.
f'(x) = 85 x^4 - 42 x^2,
so the solutions of f'(x)=0 are x=0, and +/- sqrt(42/85).
Now the second derivative f''(x) = 340 x^3 - 84 x, so the second derivative
test tells us that x=+sqrt(42/85) is a local minimum, and x=-sqrt(42/85) is a
local maximum.
f''(0)=0, so we need to classify x=0 by other means: As f(x) is an odd order
polynomial it has an equal number of maxima and minima, but here we have
three roots for f(x)=0, so f(0) must be a point of inflection.
RonL