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###### (5 points) Letf(r) = ~x" 9x' + 4x ~ 6. Find the open intervals on which f is concave up (down}; Then determine the x-coordinates of all inflection points of f.f is concave up on the intervals2 f is concave down on the intervalsThe inflection points occur at X =

(5 points) Letf(r) = ~x" 9x' + 4x ~ 6. Find the open intervals on which f is concave up (down}; Then determine the x-coordinates of all inflection points of f. f is concave up on the intervals 2 f is concave down on the intervals The inflection points occur at X =

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Extra credit Find the volne of the sulidl Tetrahexron with vetticer (0,0,0), (1.0.0}. (0,1,0} , and {0,0,1} . Hint: the tetrabedlron also he dlestrihed as the first quadrant region bounded by the [ane 4+2=...

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##### Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as delta function:22' = 8(t _ 1),2(0) = 7, 2 (0) = 0.In the following parts use h(t _ c) for the Heaviside function he(t) if necessary: Find the Laplace cransform of rhe solucion_E{r(t)}(s)b. Obrain the solution z(t)_Express the solution as piecewise-defined function and think about whac happens to che graph of the solution at t = 1.if 0 < t < 1,if 1 < t < 0.

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