DUMMYHWC MATHS 204-1 SPRING 2021 ...

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DUMMYHWC   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

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Assignment Question 
 1. Find the equation of the line tangent to the graph of  
                             F(x) = 2 + ??? at the point X=1: 
 →Solution:  we have given function  
                                               F(x) = 2 + ???                                    ……… (*) 
                        First we will find the value of F(x) at X=1 
                         ⟹                 F(1) = 2 + ??1                                        ∵ ??1 = 0 
                         ⟹                 F(1) = 2  
                          Say, F(x) = Y 
                        Now we will find line tangent at point (1, 0)       
                        Since equation of tangent,  
                                                            (Y-y)  = 
??(1)
??
(X-x)                       ……. (**) 
                        Where (a, b) is a point and  
??(?)
??
  is slope at point (x, y) 
                        Since we have point (1, 0) = (x, y) 
                        Now, we will calculate the slope at the point (1, 0)  
                        So by (*),   
                                                              F(x) = 2 + ??? 
                                               By differentiating with respect to x 
                                           ⟹           
??(?)
??
=  
1
?
        
                                                          At point x = 1     
                                           ⟹                
??(1)
??
 =   
1
1
= 1         
                                       Now by (**) at (1, 0) 
                                       We get, 
                                          ⟹                    ? − 0 = 1. (? − 1)    
                                          ⟹                      ? − ? + 1 = 0         ???????.
  2.  Find the derivative of:     F(x) = (2x+1) ( x2  – 3x)   
  ⟶ Solution : we have function  
                                              F(x) = (2x+1) ( x2  – 3x)         
                           We can write F(x), 
                                               F(x) = 2?3 − 6?2 + ?2 − 3? 
                                               F(x) = 2?3 − 5?2 − 3?                     …. (a) 
                           Now, we will differentiate (a) with respect to x 
                                     ⟹  
??(?)
??

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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