# 15 Calc Differentiation questions

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### Question Description

1.

Which one of the following does not find the value of f ′(3) for f(x) = 3x2 - 4x + 1? (4 points)

 All of these find the value for f ′(3).

2.

Use your graphing calculator to find the value of f ′(0) for f(x) = sin(x) + ex. (4 points)

 0 1 2 -1

3.

How do Curves A and B compare to each other with respect to f and f ′?

(4 points)

 The answer cannot be determined. f: Curve B, f ′: Curve A Neither Curve A or Curve B are derivatives of each other. f: Curve A, f ′: Curve B

4.

Find the equation of the line tangent to y = -x2 + 3x + 8 at x = 2. (4 points)

 y = -2x + 2 y = -x + 12 y = -x + 2 y = -2x - 12

5.

If f(x) = 2a|3x - 9| - ax, where a is some constant not equal to zero, find f ′(3). (4 points)

 0 not enough information 1 DNE

1.

Find f'(x) for f(x) = 5x2 − 3x + 12. (4 points)

 10x + 12 −10x − 3 10x − 3 None of these

2.

Find f '(−3), if f(x) = (2x2 − 7x)(−x2 − 7). Round your answer to the nearest integer. Use the hyphen symbol, -, for negative values. (4 points)

3.

Find the derivative for . (4 points)

4.

If f and g are differentiable functions for all real values of x such that f(2) = 5, g(2) = 3, f '(2) = 1, g '(2) = −2, then find h '(2) if h(x) = f(x) g(x). (4 points)

 13 −13 7 −7

5.

Find the coefficient of the squared term in the simplified form for the second derivative, f "(x) for f(x) = (x3 + 3x2 + 3)(3x3 − 6x2 − 8x + 1) . Use the hyphen symbol, -, for negative values. (4 points)

1.

If f(x) = (2x3 − 4)6, then what is f '(x)? (4 points)

 21x2(x3 − 4)5 21x8 6(2x3 − 4)5 6(2x3 − 4)5(6x2)

2.

Find f '(x) for . (4 points)

 f'(x) = cos(3x)

3.

Is the following true or false?

(4 points)

 True False

4.

Find of . (4 points)

5.

Differentiate y = sin2x − cos2x. (4 points)

 2sin(x) − 2cos(x) 2sin(x) + 2cos(x) 4sin(x)cos(x) 0

vmohanakumar
School: Cornell University

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