Asked by Jay

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?

Answers

Answered by Jay
= 0.5(-6+h)^2 + 6(-6+h)+ 7.5 - (-10.5)/h *
Answered by Reiny
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
Answered by Jay
how did you get h^2/2?
Answered by Jay
somebody? :|
Answered by Reiny
.5 is the same as 1/2, so
.5(h^2) = (1/2)h^2 = h^2/2
Answered by Jay
Oh wow thanks~

Related Questions