HWC MATHS XXXXXXXXXXSPRING 2021
XXXXXXXXXXMIDTERM TEST
NAME__________________________
1. A bank offers a 10-year CD that earns 2.45% compounded continuously.
- If $ 6000 is invested in this CD, how much will it worth in 10 years?
-How long will it take for the account to be worth $9000?
2. Find the equation of the line tangent to the graph of
F(x) = 2 + Lnx XXXXXXXXXXat the point X=1:
3. Find the derivative of: F(x) = (2x+1)(x2 – 3x)
4. Find dF/dx of F(x) =(3x + 5)/(x2 + 3)
5. Find the derivative of: F(x) = Ln(x4 +1)
6. Find y’ when y = 5(x2 – 3)2
7. Find F’(x) of F(x) = x2(X – 5)3 and find the values of x where the tangent line is horizontal.
8. Use implicit differentiation to find y’ and to evaluate Y’ at the point
(-1, 1) when y2 + 2y +3x = 0
9. Assume that x= x(t) and y= y(t), find the rate of change of
y = x3 +2 when x’ = 4 and x= 5
10. Use a graphing calculator to graph F(x) = 2x 3 -- 3x 2 -- 36x XXXXXXXXXXDetermine the intervals on which F(x) is:
Increasing
Decreasing
Concave upward
Concave downward
----------------------------------------
The local minimum
The local maximum
The point of inflection
11. Find the second derivative for F(x) = 2x3 – 4x2 + 5x -- 6
F’(x) =
The critical values F’(x) = 0
x = ___ f(x) =___
The points of inflection
F’’(x) = 0 XXXXXXXXXXx = ___ f(x) = __
12. If it’s necessary, use the Hopital’s rule to find:
Lim (5X)/ (ex – 1)
X (0
13. If it’s necessary, use the Hopital’s rule to find:
Lim (x2 – 9)/(x + 3)
x(-- 3
14. For F(x) = x3 – 6x2 + 9x – 6 in the interval [- 1, 5] find alge
aically:
F’(x) =
F’(x) = 0
F’(-1) =
F”( x ) =
F”(x) = 0
F”( 5 ) =
Absolute maximum( , XXXXXXXXXXAbsolute minimum( , )
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