Characteristics of graphs of f and f' Practice Problems Online

Given $f'(x) = x^2 + 9x + k,$ if $f(x)$ is an increasing function for all values of $x,$ what is the range of $k?$

Suppose $f(x)$ is a function such that $y=f'(x)$ is given by the curve in the above diagram. If $y= f'(x)$ is tangent to the $x$ -axis at $x=a=7,$ which of the following statements is NOT correct about $f(x)?$

Suppose $f(x)$ is a differentiable function such that the graph of $y=f'(x)$ is as shown in the above diagram. If $a = 2, b = 3, c = 5, d= 7,$ and $f'(e) = f'(d)$ for all $e \geq d,$ which of following statements is correct?

In

[-2, 2],

f(x)

attains a maximum value at

f(0)

.

f(5)

is a local maximum. There are four extreme values between

x=-3

and

x=7.

f(x)

is a linear function for

x > 7 .

Suppose $f(x)$ is a function such that the graph of $y=f'(x)$ is a line as shown in the above diagram. If $a=19,$ which of following statements is correct?

Suppose $f(x)$ is a function such that $f'(x) = K(x-a)(x-b) ,$ where $K$ is a positive constant. If $a=5$ and $b=10,$ which of following statements is NOT correct?

f(x)

is a cubic function. If

f(5)= 0,

there are two intersection points between

f(x)

and the

x

-axis.

f(5)

and

f(10)

are always

0.

f(x)

is a decreasing function on

[5,10]

.

Concept Quizzes

Challenge Quizzes

Characteristics of graphs of f and f'

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.