Pls answer true or false for questions 10,11, and 12 True/False1)If f is decreasing on (a,b) then f'(x) <0 for each x in (a,b)2) If f'(c)=0 then f has a relative minimum or a relative maximum at x = c3) Iff and g are both increasing on (a,b) then f+g is increasing on (a,b)) If ƒ and g are both decreasing on (a,b) then fg must be decreasing on (a,b)5)If the graph of f is concave upward on (a,b), then the graph of -f is concave downwardon (a,b)6) If the second derivative of f exists on (a,b) and the graph of f has an inflection point at(c, f(c)) where a b²15) If e** >0 then k>0 and x>0.16) f(x) = ex is an increasing function if k>0 and a decreasing function if k<0.17) (In x³)=3 lnx for all x in (0,00)18) If a>0 and b>0 then In(a+b) = ln a + ln b19) If b>0, then enb= ln e20) If f(x)=3" then f'(x) = x3-¹21) If f(x) = e²then f'(x) = e22) If ƒ(x) = π*then f'(x) = n*23) If f(x)=e³x² then f'(x) = ex124) f(x) = ln |x| then f'(x):25) f(x) = ln 5 then f'(x) =P26) f(x) = ln(x+5)² then f'(x) =x1(x + 5)²27) If you are modeling exponential decay, you can use a model of the form Q(t)=Qe

10) If f(x) is not continuous on the interval [a,b] then f(x) cannot have an absolute maximum value. 11) If f(x) is defined on a closed interval [a,b] then f(x) has an absolute minimum value. 12) If f(x) is continuous on [a,b], f(x) is differentiable on (a,b), and f'(x)=0 for all x in (a,b), then the absolute maximum value of f(x) on [a,b] is f(a) or f(b).

10) If f(x) is not continuous on the interval [a,b] then f(x) cannot have an absolute maximum value. 11) If f(x) is defined on a closed interval [a,b] then f(x) has an absolute minimum value. 12) If f(x) is continuous on [a,b], f(x) is differentiable on (a,b), and f'(x)=0 for all x in (a,b), then the absolute maximum value of f(x) on [a,b] is f(a) or f(b).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.3: Maxima And Minima

Problem 30E: Let f(x,y)=y22x2y+4x3+20x2. The only critical points are (2,4), (0,0), and (5,25). Which of the...

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