15 calc questions

User Generated

10fehyrf

Mathematics

Description

1.

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

2.

Find the derivative of e2x. (4 points)

3.

If f(x) = ln(1 - 5x), then find f '(x). (4 points)

4.

Find the derivative with respect to x of the quantity of e raised to the power of 3 times the natural log of x. . (4 points)

5.

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

1.

Find y' if x = tan(y). (4 points)

2.

Find dy, dx for x2 - y2 = xy. (4 points)

3.

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

4.

Find dy, dx if f(x) = (x + 2)7x. (4 points)

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(x)=4.5x23x+2

  1. Use the limit definition to find f ′(x).
  2. Use the alternate limit definition, limit as x approaches a of the quantity f of x minus f of a over the quantity x minus a 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.

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