Question

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?

Answer 1

= 0.5(-6+h)^2 + 6(-6+h)+ 7.5 - (-10.5)/h *

Answer 2

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

Answer 3

how did you get h^2/2?

Answer 4

somebody? :|

Answer 5

.5 is the same as 1/2, so
.5(h^2) = (1/2)h^2 = h^2/2

Answer 6

Oh wow thanks~