91Ó°ÊÓ

Find two possible functions \(f\) given the second- or third-order derivatives. \(f^{\prime \prime \prime}(x)=\cos x\)

Find two possible functions \(f\) given the second- or third-order derivatives. \(f^{\prime \prime \prime}(x)=8 e^{-2 x}-\sin x\)

For the following exercises, find two possible functions \(f\) given the second- or third-order derivatives. $$f^{\prime \prime \prime}(x)=8 e^{-2 x}-\sin x$$

A car is being driven at a rate of \(40 \mathrm{mph}\) when the brakes are applied. The car decelerates at a constant rate of \(10 \mathrm{ft} / \mathrm{sec}^{2} .\) How long before the car stops?

You are merging onto the freeway, accelerating at a constant rate of 12 \(\mathrm{ft} / \mathrm{sec}^{2} .\) How long does it take you to reach merging speed at 60 \(\mathrm{mph}\) ?

A car company wants to ensure its newest model can stop in 8 sec when traveling at 75 mph. If we assume constant deceleration, find the value of deceleration that accomplishes this.

A car company wants to ensure its newest model can stop in less than 450 ft when traveling at 60 \(\mathrm{mph}\) . If we assume constant deceleration, find the value of deceleration that accomplishes this.

Find the antiderivative of the function, assuming \(F(0)=0\). \(f(x)=x^{2}+2\)

For the following exercises, find the antiderivative of the function, assuming \(F(0)=0\). $$\mathbf{[T]} f(x)=x^{2}+2$$

Find the antiderivative of the function, assuming \(F(0)=0\). \(f(x)=4 x-\sqrt{x}\)