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Derivatives: Going Off On a Tangent Quiz
Think you’ve got your head wrapped around
? Put your knowledge to
the test. Good luck — the Stickman is counting on you!
The graph below shows a function
and a line:
The line is
a secant line between
a and b
f at a
f at b
none of the above
Each graph below shows a function
and a line. Which line is NOT tangent to its corresponding function?
Q. Three of the following phrases mean the same thing. Which phrase does not mean the same as the others?
slope of the tangent line to
f at a. f ' ( a)
limit of secant lines between
a and a + h as h approaches 0.
f at a
At which value of
is the slope of
closest to zero?
The graph shows a function
Which derivative is greatest?
f ' ( x 1) f ' ( x 2) f ' ( x 3) f ' ( x 4)
Q. Find the tangent line to f( x) = x 2 at -1.
y = 2 x + 1 y = -2 x + 1 y = 2 x – 1 y = -2 x – 1
is shown below:
Consider the function
Which statement is true?
We can draw a tangent line to f at x 1 but not at x 2. We can draw a tangent line to f at x 2 but not at x 1. We can draw tangent lines to f at both x 1 and x 2. We cannot draw tangent lines to f at either x 1 or x 2.
Q. Use a local linearization to approximate cos(1.5), given that the derivative of cos( x) at π/2 is -1.
Q. Which of the following statements cannot be true of any function f?
f is both continuous and differentiable. f is continuous but not differentiable. f is not continuous but is differentiable. f is neither continuous nor differentiable.