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Duplicate of Definition of Derivative Review Flashcards | StudBud

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Find the equation of the tangent line to f(x) = x2 - x at x = 2.

Is the function differentiable at x = 0?

Duplicate of Definition of Derivative Review

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Review questions for limit definition of derivative. #calculus #derivatives #longform #differentiablility

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Answers

1
Is the function differentiable at x = 0?
No, there is a discontinuity at x = 0.
No, there is a vertical tangent at x = 0.
No, there is a cusp at x = 0.
Yes, the function is differentiable at x = 0.
2
Find the equation of the tangent line to f(x) = x² - x at x = 2.
y = 3x + 4
y = 3x - 4
y = 3x + 6
y = 3x - 6
3
Is the function differentiable at x = 0?
No, the function has a cusp at x = 0.
Yes, the function is differentiable at x = 0.
No, the function has a vertical tangent at x = 0.
No, the function has a corner at x = 0.
4
Find the slope of the line tangent to f(x) = -10x² + 8x at x = 9.
-140
-172
-243
-108
5
Find the slope of the line tangent to f(x) = -1/(x + 6) at x = -4
1/4
-3/4
3/4
-1/4
6
Find the equation of the tangent line to f(x) = 48/x at x = 2.
y = -12x + 24
y = -24x + 72
y = -12x
y = -12x + 48
7
Is the function differentiable at x = -7?
No - there is a cusp at x = -7.
Yes, the function is differentiable at x = -7.
No - there is a discontinuity at x = -7.
No - there is a corner at x = -7.
8
Find the derivative of 4x² - 2.
8x
8x2 - 2
4x
8x - 2
9
Find the derivative of f(x) = x³ + 7 when x = 4.
-48
49
55
48