1. Find the equation of the line passing the points (−1, 3), (8, 2).

2. Find the equation of the line that contains (−4, 6) and is perpendicular to the line −7x + 3y = 6.

3. Consider the function f(x) = −2x2 + 4x − 1. Find all information regarding f(x) (x and y intercepts, the axis of symmetry, the vertex point). Sketch the graph of f(x).

4. Solve the exponential equations. (a) 2x2+2 = 8x

   (b) 31−2x = 45x

5. Solve the equation

(c) ex+1 = 31−3x (d) 2x+1 = 32−x

(a)f(x)=x2+x+1

8. Find the derivative of the following functions.

   (a) y=4x9 (c) y= 1(x5 +7) 2

   (b) y=−x12 (d) y=x2+1 5

9. Find g′(3) given that f(3) = −1 and f′(3) = 5. (a) g(x)=2x3 −7xf(x)

   (b) g(x) = 2x+1 f (x)

(b)f(x)= 1 x+1

(e) y=x−3 + 1 x7

(f) y=7x−6−5√x

(g) y= 2x+7 5x−1

(h) y= x+2 x2+2

220
1 + 5.5e−0.17x

= 170.

6. Solve the following logarithmic equations.
   (a) log5(x+5)=log53 (b) lnx+ln(x+1)=8

7. Use the limit definition to find to find the derivative of the following functions.

10. Find the equation of the tangent line to the graph at the specified value of x. √

    y=x 3−x2, x=1.

11. Use the derivative to find the Maximum or Minimum values of the following functions.

(a)

(b)

f(x)=2x3 −9x2 +12x−3

f(x)=x2 +5x−1

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