What Calculus Concepts Are Illustrated Through These Problem Examples?

[livestrong136]

https://www.physicsforums.com/attachment.php?attachmentid=47375&stc=1&d=1337282982
Given the following graph of the function y = ƒ(x) Find the interval(s) x value(s) for which each of the following is/are true ( Enter your answers separated by commas with no spaces. eg. A

ƒ′(x) = 0

= B, C

ƒ′(x) > 0

= D

ƒ′(x) < 0

= A


The displacement of an object is given by the equation s(t) = 2t^2 + 5 then at time:
a. t = 2 the velocity is = 13
b. t = 5 the velocity is = 55
c. t = 2.5 the velocity is = 18


For the function ƒ(x) = x^3 - 4x, what is the average rate of change between:
a. x = 3 and x = 4? = 33
b. x = 0 and x = 0.5? = -3.75

What is the simplified average rate of change between x = 2 and x = 2 + h for the function:
(Enter your expression as you would enter an equation in Winplot)
a. ƒ(x) = x2? = 4+h
b. ƒ(x) = 1/x? = -1/4+2h

For the function ƒ(x) = 2x^2 + 5, calculate f(a+h)-f(a)/h
a. x = 5
= 55
b. x = 0.1
= 5.02

 

[Joffan]

Graph question: two wrong.
Displacement & velocity - all those are wrong.
Average rate of change - both right.
(2+h) - wrong as written, but I suspect you actually have these right with better use of brackets and symbols.
f(a+h) etc - both wrong, also missing brackets in question.