Increasing vs. Decreasing

1/19/2024
Calculus:
Shively's Absent (Again?!)

Multiple Choice

Why is Shively absent?

• Car accident, I got flattened (skrr)

• Hippo fight. I kept yappin (oh no)

• Rizzed Covid in Manhatten (gross)

• Electro shock. It was zappin

  (flow glow)

Open Ended

So what happened to you this 5 1/2 day
Winter Break (Part II: The Winter-ering)?

We say a function f is strictly increasing on the open interval
(a , b) if we can show that for any sample x-values in I:

x1 being less than x2 implies y1 is less than y2.

Increasing Functions

Multiple Select

Where is f(x) increasing? Select all that apply.

• x ∈ (A, C)

• x ∈ (C, E)

• x ∈ (E, G)

Functions and Slopes

Multiple Select

This time the graph shows y = g'(x) , which is the DERIVATIVE (a graph of the slope) of the original function y = g(x).

On what intervals is the original function g(x) increasing?

• x ∈ (A, C)

• x ∈ (B, D)

• x ∈ (E, G)

• x ∈ (F, H)

• x ∈ (C, E)

Multiple Select

On what intervals is the original function g(x) decreasing?

• x ∈ (A, B)

• x ∈ (C, E)

• x ∈ (D, F)

• x ∈ (G, H)

• x ∈ (A, H)

Draw

Chill out.

Multiple Select

Given the graph of y = h'(x), the derivative of h(x), on what intervals is the graph of h(x) increasing?

• x ∈ (A, B)

• x ∈ (D, F)

• x ∈ (F, H)

• x ∈ (D, H)

Multiple Choice

Which cusp matters when defining when y = h(x) is increasing ?

• x = C

• x = F

• both

• neither

Open Ended

Why?

Multiple Select

Given what you know, consider the graph. Which curve is the derivative of the other?

Let's say y = R(x) is the red curve and y = B(x) is the blue curve.

• R(x) is the derivative of B(x).

• B(x) is the derivative of R(x).

• B = R'(x)

• R = B'(x)