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The height of a ball t seconds after It is thrown upward from a height of 7 feet and with an initial velocity of 48 feet per second is f (t) = -16t^2 + 48t + 7.


(a) Verify that f" (1) = f (2). f (1) = ft f (2) = ft

(b) According to Rolle's Theorem, what must be the velocity at some time in the interval (1, 2)?

Respuesta :

Answer:

(a)f (1) ==39, f (2) =39

(b) 0 feet/seconds

Step-by-step explanation:

The height of a ball t seconds after it is thrown upward is modeled by the equation:

[tex]f (t) = -16t^2 + 48t + 7.[/tex]

(a)

[tex]f (t) = -16t^2 + 48t + 7\\f (1) = -16(1)^2 + 48(1) + 7=39\\f (2) = -16(2)^2 + 48(2) + 7=39[/tex]

(b)Rolle's theorem states that any real-valued differentiable function that attains equal values at two distinct points must have at least one stationary point somewhere between them—that is, a point where the first derivative is zero.

The velocity at some time in the interval (1,2)=0 feet/second

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