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?

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

- Math-Help 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

- Math-Help asap please~ -
**Jay**, Thursday, December 1, 2011 at 11:40pm
how did you get h^2/2?

- Math-Help asap please~ -
**Jay**, Thursday, December 1, 2011 at 11:58pm
somebody? :|

- Math-Help 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

- Math-Help asap please~ -
**Jay**, Friday, December 2, 2011 at 12:26am
Oh wow thanks~

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