Posted by Jay on Thursday, December 1, 2011 at 10:51pm.
For each function, the point given is the maximum or minimum. Use the difference quotient to verify that the slope of the tangent at this point is zero.
a) f(x) = 0.5x^2 + 6x + 7.5; (6, 10.5)
Difference quotient is
f(a + h)  f(a)/h
m= f(a+h)  f(a)/h
= f(6+h)  f(6)/h
= 0.5(6+h)^2 + 6(6+h)+ 7  (10.5)/h
What do I do next?

MathHelp asap please~  Jay, Thursday, December 1, 2011 at 10:52pm
= 0.5(6+h)^2 + 6(6+h)+ 7.5  (10.5)/h *

MathHelp asap please~  Reiny, Thursday, December 1, 2011 at 11:28pm
just go ahead and work it out ...
m = [ .5(36  12h + h^2)  36 + 6h + 7.5 + 10.5]/h
= [ 18  6h + h^2/2  36 + 6h + 7.5 + 10.5]/h
= (h^2/2)/ h
= h/2
now as h > 0 , m = 0 
MathHelp asap please~  Jay, Thursday, December 1, 2011 at 11:40pm
how did you get h^2/2?

MathHelp asap please~  Jay, Thursday, December 1, 2011 at 11:58pm
somebody? :

MathHelp asap please~  Reiny, Friday, December 2, 2011 at 12:02am
.5 is the same as 1/2, so
.5(h^2) = (1/2)h^2 = h^2/2 
MathHelp asap please~  Jay, Friday, December 2, 2011 at 12:26am
Oh wow thanks~