If f(x) has a derivative at x = a and f\'(a) = 0 then f(x) has a relative maximu

Question

If f(x) has a derivative at x = a and f'(a) = 0 then f(x) has a relative maximum or a relative minimum at x = a. Every absolute maximum is also a relative maximum. f(x) = [x-1] has an absolute minimum at x = 1 f(x) = x+4/x-2 has a horizontal asymptote at x = 2 f(x) = x - 4/x + 2 has a vertical asymptote at x = 4 An elasticity of demand. E = 2, means an increase in price by 1% will result in an approximate drop in demand of 2%. If f"(x) is positive for a lessthanorequalto x lessthanorequalto b, then f(x) is concave up in the interval (a, b) If f'(x) > 0 for each x in the interval (-1, 1), then f is increasing on (-1, 1).. If f"(x) 0 on the interval (c, b), then the point (c, f(c)) is a point of inflection of f. If f has a relative maximum or a relative minimum at x = c, then f'(c) = 0. If f'(c)

Explanation / Answer

1)derivative of a function implies slope of it, as slope is zero imples function has maximum or minimum value hence TRUE

2)TRUE because only minimum varies

3)TRUE, hence at x=1 its value is zero

4)TRUE, at x=2 its value is infinite

5)FALSE, f(x)=0 at x=4

6)TRUE

7)TRUE, hence double derivative is positive

8)TRUE, as slope is negative function has max value

10)TRUE, same as question 1

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