# exponential function

Feb 3rd, 2012
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exponential function :Consider the function f(x) = 3^(4-x), The left hand side of the axis and the graph appears on the axis. But the represents and turn into zero by raising and the axis into negative the graph of

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(1)Differentiating with respect to (2)Differentiating with respect to since (3)Differentiating with respect to (4)Let Since (5)We have (6)Therefore, the maximum is 20 and minimum is 17(7)Therefore, the maximum is and minimum is (8)The velocity function is the derivative of the position function.The acceleration is the derivative of the velocity function. (9)The velocity function is the derivative of the position function.The acceleration is the derivative of the velocity function. (10)Differentiating with respect to The tangent equation is at (11)Differentiating with respect to The tangent equation is at (12)Differentiating with respect to And the point is So slope and point form: (13)Therefore, the line is a horizontal asymptote.Since denominator is zero when Therefore, the lines are vertical asymptote.(14)By L'Hospital's rule: (15)By L'Hospital's rule: Again by L'Hospital's rule(16)By L'Hospital's rule: Again by L'Hospital's rule(17)Differentiating with respect (18)Differentiating with respect At the point Point and slope form : (19)Volume of the cone is,Given that,Substitute in (1), we getNow substitute, andin (2), we getTherefore the height of the cone is increasing at the rate of(20)Consider The velocity function is the derivative of the position function.The object is moving to the l

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