Calculus Answers

For the function f(x)=x³-6x²-12 determine

a) intervals of increase and decrease

b) location of max and minimum points

c) interval of concavity down or up

d) locator of points of inflection

Starting from the same point, Biden starts walking eastward at 52 m/s while Trump starts running towards the south at 86 m/s. How fast is the distance between Biden and Trump increasing after 2 seconds?

Q5.Graph the following piecewise function. 𝑓(𝑥)={1−𝑥,0≤𝑥≤1 2−𝑥,1<𝑥≤2

Q4. Find the domain and graph the functions. Also tell whether they are

one-one or onto.

a. √|𝑥|

b. 1−2𝑥−𝑥2

Q3. Consider the function 𝑦=√2−√𝑥

a) Can x be negative?

b) Can √𝑥 be greater than 2?

c) What is the domain of the function?

Q2. Find the domain and range of each function.

a) 𝑓(𝑡)=𝑥21+𝑥2

b) 𝑔(𝑧)=|𝑥−3|𝑥−3

c) 𝑓(𝑥)=1√4−𝑥2

Q1. Solve the inequalities and show the solution sets on the real line.

a) −2𝑥2−𝑥+3≥0

b) 13𝑥+23<56𝑥−1

c) 3𝑥−3≥𝑥−5

d) 4<𝑥2<9

e) √(𝑥−1)2 <√4

Find a function (f) that satisfies the equation ∫_0^x▒〖f(t)dt=2cos x+3x-2〗

What value of x > -1 maximizes the integral ∫_(-1)^x▒〖t^2 (3-t) 〗 dt?

(A) Find the area of the region enclosed by x=y² and y= x-2

(B) Find the volume of the solid obtained by revolving the region (part A) about the y-axis.