Let f be the function given by f (x) x3 − 6x2 + p, where p is an arbitrary constant. Write an expression for ƒꞌ (x) and use it to find the relative maximum and minimum values of f in terms of p. Show the analysis that leads to your conclusion. =

Find the domain of the function (x) = 1/∣x + 3∣

Evaluate the function f(x) =x+2x +2 at the given values of the independent variable and simplify a. f(-1) b. f(x + 2) c. f(-x) a. f(-1)-(Simplify your answer) b. ((x+2)- (Simplify your answer) c. (-x)-(Simplify your answer)

Determine whether the function x2 +3 (x − 1)2 is even, odd or neither. h(x) =

Plot the functions x, x2, exp(-x), exp(-x2) on a single graph for x between 0 and 5. Repeat the previous question where you plot the function on four different graphs (two rows and two columns).

Use the functions below to evaluate and simplify the function compositions. ƒ1(x) = 4x2 – 3x − 1, ƒ2(x) = 7x2 - - - ƒ1(x) = 10x2 − 8, ƒç(x) = 8x2 + 3x − 2, ƒ ̃(x) = 10x – 6, f1(x) = 2x − 1, fg(x) = 5x -5, f,(x) = 4x − 1, f1(x) = 8x - 7 - 1. (f2f2)(-1) 2 10x 3x 10, f2(x) = 10x2 - 6x - 5,

Let f(x) be the function 1. Find the following: x + 4 f(9)

Determine where the function is concave upward. ​ ​f(x)x^4-2x^3+7x+5

Use calculus to sketch the graph of the function given by f(x) = 3 – x2 – 6x+4. Show all steps clearly.

Let f(x) = 3csc(4x). Find the domain and range of f(x)