Questions from General Calculus

Q: The function f (x) = sin (x + sin

The function f (x) = sin (x + sin 2x), 0 ≤ x ≤ π, arises in applications to frequency modulation (FM) synthesis. (a) Use a graph of f produced by a calculator to make a rough sketch of the graph of f...

Q: Find all points on the graph of the function f (x

Find all points on the graph of the function f (x) = 2 sin x + sin2x at which the tangent line is horizontal.

Q: If f (x) = sin x + ln x,

If f (x) = sin x + ln x, find f 9sxd. Check that your answer is reasonable by comparing the graphs of f and f ‘.

Q: If F(x) = f (g(x)),

If F(x) = f (g(x)), where f (-2) = 8, f ‘ (-2) = 4, f ‘ (5) = 3, g(5) = -2, and g’(5) = 6, find F’ (5).

Q: A table of values for f, g, f ‘, and

A table of values for f, g, f ‘, and g ‘ is given. (a) If h(x) = f (g(x)), find h’(1). (b) If H(x) = g(f(x)), find H’(1).

Q: Let f and g be the functions in Exercise 63.

Let f and g be the functions in Exercise 63. (a) If F(x) = f (f(x)), find F’(2). (b) If G(x) = g(g(x), find G’(3). Data from Exercise 63: A table of values for f,...

Q: If f and g are the functions whose graphs are shown,

If f and g are the functions whose graphs are shown, let u(x) = f (g(x), v(x) = g(f(x), and w(x) = g(g(x). Find each derivative, if it exists. If it does not exist, explain why. (a) uâ€...

Q: If f is the function whose graph is shown, let h

If f is the function whose graph is shown, let h(x) =f(f(x)) and g(x) = f(x2). Use the graph of f to estimate the value of each derivative. (a) h’ (2) (b) g’ (2)...

Q: If g is a differentiable function, find an expression for the

If g is a differentiable function, find an expression for the derivative of each of the following functions. (a) y = x g(x) (b) y = x / g(x) (c) y = g(x) / x

Q: If g(x) = f(x) ,

If g(x) = f(x) , where the graph of f is shown, evaluate g’ (3).