Problem 7
Give an example of a function where \(f^{\prime}(x) \neq 0\) and \(f^{\prime \prime}(x)=\) 0.
Problem 7
Verify that the given functions are inverses. $$ \begin{array}{l} f(x)=\frac{3}{x-5}, x \neq 5 \text { and } \\ g(x)=\frac{3+5 x}{x}, x \neq 0 \end{array} $$
Problem 7
Compute the derivative of the given function. $$f(x)=\left(4 x^{3}-x\right)^{10}$$
Problem 8
(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. $$g(x)=2 x^{2}\left(5 x^{3}\right)$$
Problem 8
Compute the derivative of the given function. $$f(t)=(3 t-2)^{5}$$
Problem 8
Explain in your own words what the second derivative "means."
Problem 8
Given \(f(7)=26\) and \(f(8)=22,\) approximate \(f^{\prime}(7)\).
Problem 8
Compute the derivative of the given function. $$g(t)=\sqrt{t} \sin t$$
Problem 8
Use the definition of the derivative to compute the derivative of the given function. $$f(x)=2 x$$
Problem 9
Compute the derivative of the given function. $$h(x)=x^{1.5}$$
