A car's speed is given by the function 𝑆(𝑡)=5𝑡+2, where 𝑆 is the speed in meters per second and 𝑡t is the time in seconds. What is the car's speed at 𝑡=3 seconds?

A company’s profit 𝑃(𝑥) in dollars from selling 𝑥 units of a product is given by 𝑃(𝑥)=−2𝑥²+12𝑥−20. How many units should the company sell to maximize its profit?

Find the slope of the tangent line to the curve 𝑦=𝑥²+3𝑥+2 at the point where 𝑥=1.

The height ℎ(𝑡) of a ball thrown into the air is given by ℎ(𝑡)=−5𝑡2+10𝑡+3, where ℎ is in meters and 𝑡 is in seconds. What is the instantaneous rate of change of the height at 𝑡=1 second?

A farmer wants to fence a rectangular field along a river. He needs to fence three sides of the rectangle (the river acts as the fourth side). If he has 100 meters of fencing material, what is the maximum area of the field?

If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is

The approximate value of [Tex]f(5.001)[/Tex], where [Tex]f(x)=x^3-7x^2+15[/Tex] is