Curve Sketching

Concept Quizzes

Curve Sketching Warmup
Turning Points
Curve Sketching
Increasing / Decreasing Functions
Vertical Asymptotes
Relative Magnitude of Functions
Tangent to a Curve
Normal to a Curve

Challenge Quizzes

Curve Sketching: Level 3 Challenges
Curve Sketching: Level 4 Challenges

Curve Sketching Warmup

The graph of $y = f(x)$ is shown. On which intervals is $f'(x) > 0?$

(0,1) \text{ and } (1,2)

(0,1) \text{ and } (3, 4)

Show explanation

by Brilliant Staff

The graphs of $y = g(x)$ and $y = h(x)$ are shown above. Which is the derivative of the other?

g

is the derivative of

h

h

is the derivative of

g

Show explanation

by Brilliant Staff

The graph of $y = g'(x)$ (the derivative of $g(x)!)$ is shown. At what value of $x$ does $g(x)$ obtain a local maximum?

1 2 3 4

Show explanation

by Brilliant Staff

On what intervals is $f(x) = x^3 - 12x$ increasing?

$A = (-\infty, -2)$

$B = (-2, 2)$

$C = (2, \infty)$

B A and C A, B, and C

Show explanation

by Brilliant Staff

A penguin is climbing up a long slippery slope, taking occasional breaks to slide back down for a bit. The penguin's vertical height (in meters) above a fixed point at time $t$ minutes after starting is represented by $f(t).$ Based on the information about $f'(t)$ in the table below, at which of these times did the penguin's height reach a local minimum?

Interval	Sign of $f'(t)$
$(0,1)$	+
$(1,2)$	-
$(2,3)$	-
$(3,4)$	+

1 2 3 4

Show explanation

by Brilliant Staff

Problem Loading...

Note Loading...

Set Loading...