a. For what values of x is the function increasing/decreasing?
b. For what values of x is the graph of the function concave up/down?
c. Where they exist, find all relative extreme points, inflection points, and asymptotes.
Consider the function: f(x)=x^3+6x^2+9x?
- Posted:
- 3+ months ago by znvoith
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- down, science, math, graph, mathematics, mathematician, algebra
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Answers (1)
f'(x)=derivative of f(x), f''(x)=derivative of f'(x)
a)you have to derive the function, for f'(x)<0, function is decreasing, for f'(x)>0, function is increasing, and 0means the function is constant, so:f'(x)=3x^2+12x+9, f'(x)<0 in ]-3;-1[, so f(x) is decreasing in that area, its constant in -3 and -1, and its increasing everywhere else.
b)just do the derivative of the derivative and then aply the same process, when f''(x)<0, f(x) is concave downwards and vice-versa, te 0 is the turning point
c)the extremes are the 0 in the first question, so -1 and -3 and there are no asymptotes for this function. i'm not sure what inflexion points are though, can't help you with that