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julie and Annie each throw a softball into the air. The function f, where f(x)=3+18x−5x2, gives the height of Julie's softball, in meters, x seconds after throwing the ball.The graph represents the height of Annie's softball, in meters, x seconds after throwing the softball..

julie and Annie each throw a softball into the air The function f where fx318x5x2 gives the height of Julies softball in meters x seconds after throwing the bal class=

Respuesta :

Given,

The function for the height of the ball is f(x) = 3+18x−5x^2.

Required

The maximum height of the ball.

The maximum height of the ball is obtained by derivative of the height function and equate it to 0.

Differentiating the function with respect to x,

[tex]\begin{gathered} f(x)=3+18x-5x^2 \\ f^{\prime}(x)=\frac{d}{dx}(3+18x-5x^2) \\ f^{\prime}(x)=0+18-10x \\ f^{\prime}(x)=18-10x \end{gathered}[/tex]

Taking f'(x) =0 then,

[tex]undefined[/tex]

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