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
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
- 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~
Answer This Question
More Related Questions
- Math - determining minimums and maximums Approximate the local minimum points ...
- Math - 1. The slope of the tangent line to a function at a point is equivalent ...
- calc - let f be function given by f(x)= Ln(x)/x for all x> 0. the dervative ...
- Calculus - I have a two part question that pertains to a curve (r(x)) and its ...
- calculus - 8. Find the derivative of the function f(x) = cos^2(x) + tan^2(x) 9...
- Calculus - Explain the global optimization process for a continuous function ...
- Calc AB - Suppose that f(x) is an invertible function (that is, has an inverse ...
- calculus - 1. Which of the following expressions is the definition of the ...
- Math - Find the function f, given that the slope of the tangent line at any ...
- math calc. asap asap please - the point on the curve is 4y=x^2 nearest to (7,2) ...