Calculus Answers

Locate the absolute maximum and minimum for each of the following functions and justify your responses. (Show all work and justify)

 𝑓(𝑥) = (Cube root of x^2) − 𝑥 on the interval [−1,1]

Find the first six terms of the sequence. a₁ = -4, a_n = a_n-1 + 7

Your friend Eliza asks your help in drawing rough sketch of the graph of

𝑃(𝑥) = −(𝑥 − 1)(𝑥 + 3)2 by means of the Leading Coefficient Test. How will you 

explain the behavior of the graph?

The cable of suspension bridge hangs in the shape of a parabola.the towers supporting the cable are 400 ft apart and 150 ft high .if the cable at its lowest is 30 ft above the bridge at its midpoint ,how high is the cable 50 ft away (horizontally) from either tower?

Locate the absolute maximum and minimum for each of the following functions and justify your responses. Be careful on your differentiation, especially with #2. Show all work and justify all answers

Question 1-

f(x)= (cube root of x^2)-x on the interval [-1,1]

Question 2-

𝑔(𝑥) = 𝑥𝑒^2𝑥 on the interval [−2,0] 

Kim(x,y)->(0,0) sinx/y exist.is it true or false. Give reasons for your answer

a child has made a cubical region R which is bounded by the coordinate planes and the planes x=4 y=4 and z=4 in the first octant only. determine the average value of the function f=x^3y^3z^3 over this region R

1. The electromotive force for an electric circuit with a simplified generator

is given by 𝑓(𝑡) = 40 sin 150 𝜋𝑡 where 𝑓(𝑡) Volts is present at 𝑡 seconds.

(a) Identify the amplitude, period, and frequency of the function.

(b) Find the maximum and minimum voltages

Given g(n)-2n-5;f(n)=3n-4. Find (g°f)(-2n)

Locate the absolute maximum and minimum for each of the following functions and justify your responses. Be careful on your differentiation and show all work with calculus justification!

 a) 𝑓(𝑥) = (Cube root of x^2) − 𝑥 on the interval [−1,1]

b) 𝑔(𝑥) = 𝑥𝑒^2𝑥 on the interval [−2,0]

For each of the following functions, respond to the given prompts. Show all work that leads to your responses. With calculus justification!

a. On what interval(s), is 𝑓(𝑥) increasing? Show all work with calculus justification

b. At what value(s) of 𝑥 does 𝑓(𝑥) have a relative minimum? Show all work with calculus justification

c. On what interval(s), is 𝑓(𝑥) decreasing and concave up? Show all work with calculus justification