Not sure how to approach this problem

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kory

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Suppose that [math]f'(x)=5x[/math] [math]^\frac45 -6x[/math] [math]^\frac67[/math] . Evaluate each of the following
[math]f'(1)[/math][math]f'(6)[/math]

Should I plug in the values, use the product rule and then differentiate?...Or should I differenciate and then plug in the values after?. Im not quite sure how to attack this problem.
 

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kory said:
Suppose that [math]f'(x)=5x[/math] [math]^\frac45 -6x[/math] [math]^\frac67[/math] . Evaluate each of the following
[math]f'(1)[/math][math]f'(6)[/math]

Should I plug in the values, use the product rule and then differentiate?...Or should I differenciate and then plug in the values after?. Im not quite sure how to attack this problem.
Click to expand...
1. You have a typo - you wrote that a derivative is given instead of a function.
2. If you use the first approach, what do you get after you plug in the values?
 
Ok...So back to my first question...Do I differenciate first, then apply the quotient rule and then plug in values?...
 
kory said:
Ok...So back to my first question...Do I differenciate first, then apply the quotient rule and then plug in values?...
Click to expand...
Differentiate first. Not sure what you mean by "then apply quotient rule".
 
kory said:
Ok...So back to my first question...Do I differenciate first, then apply the quotient rule and then plug in values?...
Click to expand...
So, back to the question you were asked!
You wrote
"\(\displaystyle f'(x)= 5x^{4/5}- 6x^{6/7}\)"

If that was what you meant then \(\displaystyle f'(1)= 5(1^{4/5})+ 6(1^{6/7})= 5+ 6=11\) and \(\displaystyle f'(6)= 5(6^{4/5})+ 6(6^{6/7})= 5\sqrt[5]{6^4}+ 6\sqrt[7]{6^6}\).

If, in fact, you meant \(\displaystyle f(x)= 5x^{4/5}- 6x^{6/7}\) then \(\displaystyle f'(x)= 5(4/5)x^{4/5- 1}- 6(6/7)x^{6/7- 1}= 4x^{-1/5}- \frac{36}{7}x^{-1/7}\).
 
[math]- 36/7[/math] [math]x[/math] ^ -1/7 is exactly what I got as well but the web assignment is not agreeing...I'm missing something
 
It says "Can't raise a negative number to a non-integer power"
 
kory said:
[math]- 36/7[/math] [math]x[/math] ^ -1/7 is exactly what I got as well but the web assignment is not agreeing...I'm missing something
Click to expand...
But that is not what Halls said.

When things look messy, substitute variables

[MATH]f(x) = 5x^{4/5} - 6x^{6/7} = 5u - 6v \implies f'(x) = 5 * \dfrac{du}{dx} - 6 * \dfrac{dv}{dx}.[/MATH]
Your answer has but one term, not two.

Calculate du/dx and dv/dx.
 
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6 is not a negative number.

Do they want an exact answer or an approximation?
 
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kory said:
Suppose that [math]f'(x)=5x[/math] [math]^\frac45 -6x[/math] [math]^\frac67[/math] . Evaluate each of the following
[math]f'(1)[/math][math]f'(6)[/math]

Should I plug in the values, use the product rule and then differentiate?...Or should I differenciate and then plug in the values after?. Im not quite sure how to attack this problem.
Click to expand...
If you use the product rule, then you differentiated already. Do not differentiate again.
If you evaluate the function at a particular number you will get a constant. If you then differentiate that constant you will get 0, since the derivative of a constant is 0.

If you were really given f'(x) and want f'(1), then you evaluate the f' function at x=1.
 
kory said:
Id assume it has to be the exact number...
Click to expand...
Then why are you messing around with a calculator?

Let’s start by getting the exact statement of the derivative.

[MATH]- \dfrac{36}{7} * x^{-1/7} = - \dfrac{36}{7\sqrt[7]{x}}[/MATH] is only part of the derivative. Did you understand my post 12?
 
lev888 said:
1. You have a typo - you wrote that a derivative is given instead of a function.
2. If you use the first approach, what do you get after you plug in the values?
Click to expand...
lev, I think that we should not say/imply that a derivative is not a function.
 
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