1. ## Tangent Problems

I would have put this in the same thread as my other ones, but I've been told that its better not to clutter up one thread with too many questions. Here are two more practice problems I was having trouble with.

For this one, I'm not sure what I should do. It seems that I should be applying the Sum, Difference, and Constant Rules, but I'm not sure where I should begin with this one.

For example, for (a), should I simply add f(x) + g(x) and plug in 2 for the x value?
(6x+2) + (6x-2) = 12x = 24? I know thats probably wrong as it seems too easy to be the solution to the question.

2. You have a mistake in the algebra.
$\dfrac{{\sqrt {11x + 11h} - \sqrt {11x} }}
{h} = \dfrac{{11h}}
{{h\left( {\sqrt {11x + 11h} + \sqrt {11x} } \right)}} = \dfrac{{11}}
{{\left( {\sqrt {11x + 11h} + \sqrt {11x} } \right)}}$

Now $\displaystyle\lim _{h \to 0} \frac{{11}}
{{\left( {\sqrt {11x + 11h} + \sqrt {11x} } \right)}} = \frac{{11}}
{{2\sqrt {11x} }}$

3. For the second one, I'm not sure, but this is what I would do:

$y = f(x) + g(x)$

$\dfrac{dy}{dx} = \dfrac{d}{dx}(f(x) + g(x))$

This gives:

$\dfrac{dy}{dx} = f'(x) + g'(x))$

$\dfrac{dy}{dx} = 6+6 = 12$

(6 and 6 from the gradients of the tangents)

Ok, now when x = 2, y1 = 14
When x = 2, y2 = 10

(Those y coordinates are from the equations of the two tangent equations)

So, the y coordinate of f(x) + g(x) = 10 + 14 = 24

Hence, we get:

$\displaystyle \int^y_{24}\ dy = \int^x_2 12\ dx$

This gives: y - 24 = 12x - 24

y = 12x

4. @Unknown008;581689
I think that if you are going to offer help you should consider the level of the question.
This question is clearly a very basic almost pre-derivative question.
Therefore, giving an answer involving derivatives let alone integrals is not helpful.

5. Originally Posted by Plato
@Unknown008;581689
I think that if you are going to offer help you should consider the level of the question.
This question is clearly a very basic almost pre-derivative question.
Therefore, giving an answer involving derivatives let alone integrals is not helpful.
Yes, sorry... it's just that in my educational system, we were taught directly derivatives and integrals. The limits definition for example, was never taught to me. It's only a while ago that I learned a little more about it and how it worked. I'll be more careful next time.