15 calc questions

15 calc questions

1.

If f(x) = 7x⁶cos^-1x, find f ‘(x). (4 points)

	42x5cos-1x + 7x6
	42x5cos-1x – 7x6
	42x5cos-1x – 7x6cos-2x
	42x5cos-1x + 7x6

2.

Find the derivative of e^2x. (4 points)

	2xe2x
	2e2x
	e2x
	2ex

3.

If f(x) = ln(1 – 5x), then find f ‘(x). (4 points)

4.

Find . (4 points)

	e3lnx
	3e3lnx
	3x2

5.

For f(x) = e^cos(x) use your graphing calculator to find the number of zeros for f ‘(x) on the closed interval [0, 2π]. (4 points)

	1
	2
	3
	4

1.

Find y’ if x = tan(y). (4 points)

	cos2(y)
	sec2(y)
	0
	sin2(y)

2.

Find for x² – y² = xy. (4 points)

	2x – 2y
	0

3.

If 3x² + y² = 7 then evaluate when x = 1 and y = 2. Round your answer to 2 decimal places. Use the hyphen symbol, -, for negative values. (4 points)

4.

Find if f(x) = (x + 2)^7x. (4 points)

	7x(x + 2)(7x – 1)
	7xln(x + 2)

5.

Find the slope of the graph of the relation 2x³ – 3xy + y³ = -1 at the point (2, -3). (4 points)

You may not use your calculator for these questions.

$f\left(x\right)=4.5x^2–3x+2$

1. Use the limit definition to find f ′(x).
2. Use the alternate limit definition, with a = 2, to find the value of f ′(2).
3. Use the shortcut rules to find f ′(x).
4. Find where the tangent line to f(x) is horizontal.
5. Write the equation of the tangent line at x = 2.