Derivative Essay Examples

derivative = e-x22+e-x22.x2it follows that when 0=e-x22(x2-1)x=±1f(1)=1√eThe points of inflections are (1, 1/√e) and (-1, 1/√e) b).f(x)=x+2sinxfirst derivative =1+2cos x Second derivative =2sinxGetting the local maxima and minima we equate the first derivative to zero 1+2cos x=0cos x=-12x=2π3, 4π3 evaluating the second derivative at x=2π3 and x=4π3-2sin2π3 =-2sin32=-√3. Therefore x=2π3 is a maximum value -2sin4π3 =-2sin-32=√3And x=4π3 minimum C. f(x)=x13(x+4)The first derivative =x13ddx(x+4)+x+4ddxx13=x13+(x+4)(13x23)=x13+(x3x23+43x23)f'(x)=43x23+4x133Using the product rule to get the second derivative...

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derivative: f’(x)=-3x2 f’(X)= 0 0=-3x2 X=0 For absolute minima and maxima; f(0)=2-(0)3=2 f(-2)=2-(-2)3=10 f(1)=2-(1)3=1 Therefore: abs minima =1 at x=1 Abs maxima=10 at x=-2 (d) Calculate the limits of the following limx→0x+5x2 Solution Divide both numerator and denominator by x2 =lim x->0 1/x+5/x2 Since we have 0 in the denominator, the limit=0 (e) evaluate A'(x) at x = 1, 2, and 3. A(x) = -3x 2t dtSolution =d/dx(t2) At x=1; (12)-(-32) =-5 At x=2; (22)-(-32) =-2 At x=3;(32)-(-32) =12 (f) . Let A(x) represent the area bounded by the graph and the horizontal axis and vertical lines at t=0 and t=x for the graph in Fig. 25. Evaluate A(x) for x = 1, 2, 3, 4, and...

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derivative of at 1. (g∘f)′(1)=g′(f(1))f′(1) =g′(e)f′(1) =(2e−4)(e) =2e2−4e (d) Find the differential of . Find , an equation of the tangent line to the graph of at y = mx + c y = 2 x = 2 m = 0.42 c = 1.16 y = 0.42x+c Two cars start moving from the same point. One travels east at a constant rate of 60 miles per hour and the other travels north at a constant rate of 70 miles per hour. Find the rate at which the distance between the cars is changing 1 hour later. You may round your answer to two digits after the decimal sign. Distance = Rate x Time A = 60 x 1 = 60 Miles B = 70 x 1 = 70 Miles 3619508953500 70 z 60 x2+y2=z23600 + 4900 = z2 Z = 92.20 X =...

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derivative when occupational research is reviewed. This framework construction enables the development of valid hypotheses that functionalize subjective warrant along with inviting the observation of researchers. Q3 What principles do you believe should guide the government regulation of dangerous practices? The government should apply the rule of an arrest warrant to the criminal. An arrest warrant should be issued by the judge to the authorized officer after being assured that an individual has committed an offense. The authorized officer should then take action according to the directives issued (Riccucci 378). On the other hand, it is necessary for the judge to give summons to an individual...