Problem 9
If \(f(x)\) describes a position function, then \(f^{\prime}(x)\) describes what kind of function? What kind of function is \(f^{\prime \prime}(x) ?\)
Problem 9
Compute the derivative of the given function. $$h(x)=x^{1.5}$$
Problem 9
(a) Use the Product Rule to differentiate the function. (b) Manipulate the function algebraically and differentiate without the Product Rule. (c) Show that the answers from (a) and (b) are equivalent. $$h(s)=(2 s-1)(s+4)$$
Problem 9
Use the definition of the derivative to compute the derivative of the given function. $$f(t)=4-3 t$$
Problem 9
Compute the derivative of the given function. $$g(\theta)=(\sin \theta+\cos \theta)^{3}$$
Problem 10
Compute the derivative of the given function. $$f(x)=x^{\pi}+x^{1.9}+\pi^{1.9}$$
Problem 10
(a) Use the Product Rule to differentiate the function. (b) Manipulate the function algebraically and differentiate without the Product Rule. (c) Show that the answers from (a) and (b) are equivalent. $$f(x)=\left(x^{2}+5\right)\left(3-x^{3}\right)$$
Problem 10
Use the definition of the derivative to compute the derivative of the given function. $$g(x)=x^{2}$$
Problem 10
Let \(V(x)\) measure the volume, in decibels, measured inside a restaurant with \(x\) customers. What are the units of \(V^{\prime}(x) ?\)
Problem 10
Let \(f(x)\) be a function measured in pounds, where \(x\) is measured in feet. What are the units of \(f^{\prime \prime}(x) ?\)
