Question

Let $ A(x)=\int_{0}^{x} f(t) d t $ for $ f(x) $ in the following figure. Calculate $ A(1), A(4), A^{\prime}(1) $, and $ A^{\prime}(4) $. (Use decimal notation. Give your answers to one decimal place if needed.) \[ A(1)= \] $ \square $ $ \square $ \[ A(4)= \] $ \square $ \[ A^{\prime}(1)= \] $ \square $ $ \square $ \[ A^{\prime}(4)= \] $ \square $ Find formulas for $ A(x) $ on $ [0,2] $ and $ (2,4] $. (Express numbers in exact form. Use symbolic notation and fractions where needed.) \[ \text { on }[0,2], A(x)=4 x-\frac{x^{2}}{2} \] $ \square $ Incorrect \[ \text { on }(2,4], A(x)=2 x+6 \] $ \square $ Incorrect

          Let \( A(x)=\int_{0}^{x} f(t) d t \) for \( f(x) \) in the following figure.

Calculate \( A(1), A(4), A^{\prime}(1) \), and \( A^{\prime}(4) \).
(Use decimal notation. Give your answers to one decimal place if needed.)
\[
A(1)=
\]
\( \square \)
\( \square \)
\[
A(4)=
\]
\( \square \)
\[
A^{\prime}(1)=
\]
\( \square \)
\( \square \)
\[
A^{\prime}(4)=
\]
\( \square \)
Find formulas for \( A(x) \) on \( [0,2] \) and \( (2,4] \).
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
\[
\text { on }[0,2], A(x)=4 x-\frac{x^{2}}{2}
\]
\( \square \)
Incorrect
\[
\text { on }(2,4], A(x)=2 x+6
\]
\( \square \)
Incorrect

$Let A(x)=∫0^x f(t) d t for f(x) in the following figure. Calculate A(1), A(4), A^'(1), and A^'(4). (Use decimal notation. Give your answers to one decimal place if needed.) A(1)= □ □ A(4)= □ A^'(1)= □ □ A^'(4)= □ Find formulas for A(x) on [0,2] and (2,4]. (Express numbers in exact form. Use symbolic notation and fractions where needed.) on [0,2], A(x)=4 x-(x^2)/(2) □ Incorrect on (2,4], A(x)=2 x+6 □ Incorrect$

Added by Brittany M.

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