Help me with some calculus questions which I couldn't go through...
a) Find the intervals on which function is increasing and decreasing ?
f(x) = x^3 - 3x^2
b) Find the intervals on which function is increasing and decreasing ?
f(x) = 1 / x^2
c) what are critical numbers for:
i) f(x) = x^3 - 3x^2 and
ii) f(x) = 3x^4 - 4x^3
d) For which interval the function f(x) = 8x^3 - 2x^4 is concave downwards?
e) Find the points of inflection for f(x) = x^4 - x^3 ...
Find the first derivative of your function, set the equal to zero and solve for x. Those are your critical points.
The function is concave down when for all values of on a given interval. When the function changes concavity you have your inflection points.d) For which interval the function f(x) = 8x^3 - 2x^4 is concave downwards?
e) Find the points of inflection for f(x) = x^4 - x^3 ...