2. Find the coordinates of the point where the line tangent to the parabola 2

Size: px

Start display at page:

Download "2. Find the coordinates of the point where the line tangent to the parabola 2"

Darlene Parks
5 years ago
Views:

1 00. lim = (B) (C) 0 (D) (E). Find the coordinates of the point where the line tangent to the parabola y = 4 at = 4 intersects the ais of symmetry of the parabola. 3. If f () = 7 and f () = 3, then the eqation of the tangent to the crve y = f( ) at = is y = 3+ 3 (B) y = 3+ 3 (C) y = (D) y = 7 (E) y = On the interval < <, the crve 3 y = is increasing and concave p (B) increasing and concave down (C) decreasing and concave p (D) decreasing and concave down (E) horizontal. The minimm vale of the fnction f ( ) 4a a 3 = + +, a > 0, is a (B) 6a (E) none of the above 3 (C) 3 a (D) a 6. A fnction is defined for all real nmbers and has the following property: 3 f ( + h) f( ) = 4 h+ h 6 h. Find f ( 3).

2 00 7. For what positive vale of k is the line y = 9+ k tangent to the crve y 3 = 6? 8. A rectanglar field is to be fenced off along the bank of a river, and no fence is reqired along the river. If the material for the fence costs $.00 per foot for the two ends and $7.0 per foot for the side parallel to the river, find the dimensions of the field of largest possible area that can be enclosed with $9, worth of fence lim 0 + = (B) 0 (C) (D) 0 (E) 0. The -coordinate of the point where the tangent to the parabola (not a verte) intersects the -ais is y = a at = p p (B) p (C) ap (D) ap a (E) p. f ( ) g ( ) f ( ) g ( ) The table above shows some of the vales of two differentiable fnctions f and g and their derivatives. If h ( ) = f( g ) ( ), then h () = (B) 7 (C) 4 (D) 0 (E) 6. Using the vales in the table from the previos problem, if h ( ) f( g ( )) h (4) = =, then 4 (B) 7 (C) (D) 0 (E)

3 If f ( ) is a continos fnction and f () = 7 and f () = 3, then f (.0) is approimately 6.03 (B) 6.9 (C) 6.97 (D) 7.0 (E) Consider the crve ( ) 3 y 3 k 6k = + +, k >. On the interval < < k, y is positive, and y is first positive, then negative (B) y is positive, and y is first negative, then positive (C) y is negative, and y is first positive, then negative (D) y is negative, and y is first negative, then positive (E) Neither the sign of y nor the sign of y can be determined withot knowing the vale of k.. A cbe is epanding so that its srface area is increasing at a constant rate of 9 in /sec. How fast is the volme increasing at the instant when the srface area is 08 in? Show nits in yor answer. 6. Rnner B is 7.3 yards behind Rnner A. Both are rnning at 9 yards/sec. At this point, A tires and decelerates at 0. yards/sec. B picks p speed, accelerating at 0. yards/sec. If they contine like this, how many more yards does Rnner A cover before the two rnners are side by side? (Give yor answer ronded to the nearest tenth of a yard). 7. If f( ) = and , which of the following is closest to f (3)?.68 (B).97 (C) (D) 3 (E).6

4 y y = f ( ) Pictred above is the graph of f ( ). For what vales of is the graph of f ( ) concave down? < < (B) < 4 or 0 < < 4 (C) 4 < < 4 (D) all vales of (E) the graph of f ( ) is always concave p 9. g ( ) g ( ) If g ( ) and g ( ) have the vales shown in the table above, and then f () = f ( ) = g ( ), (B) 6 (C) 3 (D) 4 (E) If 0 4 f( ) d= 0, 0 f( ) d= 9, and 7 4 f ( d= ), then 7 f ( d= ) (B) (C) (D) 3 (E) 4

5 00. If = +, then + d = d (B) d (C) d (D) d (E) d. The average area of all circles with radii between 3 and 6 is π (B) 7 π (C) 8π (D) π (B) 4 π 3. A rmor spreads continosly at the rate of 3t + 6t (where t is measred in days). How many people hear the rmor on the third day? (B) 34 (C) 44 (D) 4 (E) 4 4. Find the total area of all regions bonded by the graphs of y = sin and y = tan over the interval π π.. If [ f ] lim ln ( ) =, then lim f ( ) = 0 (B) ln (C) (D) (E) e 6. The point Aa (, b ) is on the parabola y =. Point V is the verte of the parabola. Point C(0, c ) is the point where the perpendiclar bisector of AV intersects the y-ais. Find lim c. a 0

6 The graph of y = f ( ), shown to the right, consists of two straight line segments. If f (0) = 0, then in the vicinity of which of the following vales of the crve y = f( ) is falling and concave down? y y = f ( ) (B) 4 (C) 6 (D) 8 (E) 0 8. If f ( ) = sin cos 3 and k is an odd integer, then f ( kπ ) = (B) (C) (D) (E) 9. If 4 F( ) = dt, then F () e = + lnt e (B) ln (C) (D) e (E) e 30. If the slope of the tangent to the crve at any point (, y ) on the crve eqals y, what kind of crve can it be? a circle (B) a parabola (C) an ellipse (D) a hyperbola (E) none of the above 3. How mch shold be invested today to accmlate $0,000 in seven years at % annal interest, componded continosly? 3. In the year 000, the yearly consmption of oil throghot the world was approimately billion barrels and increasing eponentially at a rate of %. Assming the world s total oil reserves are one trillion barrels, in what year will the oil reserves be depleted?

m = Average Rate of Change (Secant Slope) Example:

m = Average Rate of Change (Secant Slope) Example: Average Rate o Change Secant Slope Deinition: The average change secant slope o a nction over a particlar interval [a, b] or [a, ]. Eample: What is the average rate o change o the nction over the interval