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...

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HWC MATHS 204-1 SPRING 2021 MIDTERM 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 at 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 Determine 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 x = ___ 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 algebraically: F’(x) = F’(x) = 0 F’(-1) = F”( x ) = F”(x) = 0 F”( 5 ) = Absolute maximum( , ) Absolute minimum( , ) PAGE 4