MHB Evaluating Trigonometric Expressions

[mathdad]

Given h(x) = tan x, evaluate dh/dx on [pi/4, 1].

Note: d = delta

I need one or two hints. I can then try on my own.

 

[tkhunny]

Given h(x) = tan x, evaluate dh/dx on [pi/4, 1].

Note: d = delta

I need one or two hints. I can then try on my own.

You'll have to do better than that. Are we required to use the Definition of the Derivative? Is this a Mean Value problem? How does one "evaluate" on a range?

 

[skeeter]

Given h(x) = tan x, evaluate dh/dx on [pi/4, 1].

Note: d = delta

I need one or two hints. I can then try on my own.

$\dfrac{\Delta h}{\Delta x} = \dfrac{h(1) - h\left(\frac{\pi}{4}\right)}{1 - \frac{\pi}{4}}$

Note: learn some Latex ...

 

[mathdad]

You'll have to do better than that. Are we required to use the Definition of the Derivative? Is this a Mean Value problem? How does one "evaluate" on a range?

Skeeter got it. No derivative required. This question comes from my precalculus textbook by David Cohen. No calculus needed here. I was just not sure how to start the calculation. Like I said, Skeeter got it.

 

[mathdad]

Ok.

The set up is:

[tan 1 - tan (π/4)]/(1 - π/4)

I will do it tonight after work.

 

[tkhunny]

So it is a Mean Value problem. Fair enough.

 

[mathdad]

So it is a Mean Value problem. Fair enough.

Is it more a rate of change problem?

 

[tkhunny]

Is it more a rate of change problem?

Right. An Average Rate of Change, aka Mean Value. Anyway it is done,

 

[mathdad]

It is done as far as this question is concerned. There are about 5 or 6 similar questions in Section 6.3 in my book that I can now do thanks to this site.

 

[Prove It]

Right. An Average Rate of Change, aka Mean Value. Anyway it is done,

An Average Rate of Change is NOT called a Mean Value.

The Mean Value Theorem states that the Average Rate of Change is equal to the gradient of the function at some point within the interval. It's poorly named too, as it is most likely not the "mean value" which gives that same gradient.

 

[mathdad]

Good information.