# Derivative Essay Examples

## Problem Solving

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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...

• Words: 825
• Pages: 3

## HOME WORK

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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...

• Words: 275
• Pages: 1

## 983176648 test 3 revised

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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 =...

• Words: 550
• Pages: 2