Could Someone help:Calculus (1 Viewer)

[Testpilot]

Could somebody please help me answer these questions. Thanks. Sorry thats its in a word doc.

 

[webby234]

Q1 looks good except for x = 2 you had y = 4/3 instead of -4/3.
Also you did not find point of inflexion, only x value. (y value will be -2/3)

Q2 - basically - you need to show it touches the curve once.

x - 4 = x² - 5x + 5
x² - 6x + 9 = 0

b² - 4ac
= 36 - 36
= 0
so one solution.

As there is one point where the line touches the curve it is a tangent

 

[webby234]

Q3 - m_t = -1/m_n

so gradient is -1

The point of intersection between curve and tangent is (3,-1) - solve them simultaneously as I have started above.

so y = mx + b
-1 = -3 + b
b = 2

y = -x + 2 as required.

 

[Testpilot]

thanks