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you are trying out a new car. after t minutes, it has traveled f(t) = t ⁴/³ miles. What is its acceleration when t = 27?

User Sula
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3 votes

Answer:

when t = 27, the acceleration of the car is 4

Explanation:

To find the acceleration of the car when t = 27, we need to differentiate the function f(t) = t^(4/3) with respect to t.

Differentiating f(t) = t^(4/3) involves using the power rule of differentiation, where the derivative of t^n with respect to t is given by n*t^(n-1).

Applying the power rule, we get:

f'(t) = (4/3)*t^(4/3 - 1)

Simplifying the exponent, we have:

f'(t) = (4/3)*t^(1/3)

Now, let's substitute t = 27 into the expression for f'(t) to find the acceleration:

f'(27) = (4/3)*(27)^(1/3)

Evaluating the exponent, we get:

f'(27) = (4/3)*(3)

Simplifying the fraction, we have:

f'(27) = 4

Therefore, when t = 27, the acceleration of the car is 4.

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