15 Calc Differentiation questions

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).

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

	0
	1
	2
	-1

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

Graph A increases from the left to cross the x axis near 0.6. Graph B is increasing from left to right, crossing the x axis at about 0.2, then crossing the y axis around 1, decreases to cross the x axis around 0.8 and then increasing, crossing the x axis around 1 (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

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

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

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

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

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)

Find the derivative dy over dx for y equals the quotient of the quantity x squared minus 2 times x and the quantity x cubed plus 3. . (4 points)

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

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)

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)

Find f ‘(x) for f of x equals the square root of the quantity cosine of 6 times x . (4 points)




	f'(x) = cos(3x)

Is the following true or false?

the second derivative of the quantity x squared times the cosine of x equals 2 times cosine x minus 4 times x times sine of x minus x squared times cosine x (4 points)