SOLUTION: FIND THE AVERAGE RATE OF CHANGE OF f(x)=-2X^2+× FROM 0 TO 3 AND FIND THE EQUATION OF THE SECANT LINE CONTAINING (0, f(0)) and (3, f(3))

Algebra ->  Equations -> SOLUTION: FIND THE AVERAGE RATE OF CHANGE OF f(x)=-2X^2+× FROM 0 TO 3 AND FIND THE EQUATION OF THE SECANT LINE CONTAINING (0, f(0)) and (3, f(3))      Log On


   

Question 669056: FIND THE AVERAGE RATE OF CHANGE OF f(x)=-2X^2+× FROM 0 TO 3 AND FIND THE EQUATION OF THE SECANT LINE CONTAINING (0, f(0)) and (3, f(3))
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%283%29=-2%2A3%5E2%2B3+
f%283%29=-2%2A9%2B3+
f%283%29=-18%2B3+
f%283%29=-15+
now find
f%280%29=-2%2A0%5E2%2B0+
f%280%29=0+

so, the points are:
(0, f%280%29) =(0, 0)
and (3, f%283%29) =(3, -15)

now find a slope:
f%283%29-f%280%29%2F%283-0%29=%28-15-0%29%2F3=-15%2F3=-5........the slope is m=-5
Equation of the line thru (0,0) and with slope m=-5
Equation Form: y+=+mx+%2B+b
0+=+-5%2A0+%2B+b
b+=+0
Equation of the secant: y+=+-5x
here is a graph:
+graph%28+600%2C+600%2C+-10%2C+10%2C+-20%2C+10%2C-2x%5E2%2Bx%2C-5x%29+