find the gradient at the following points at the given (part2)

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October 9th 2011, 04:52 AM
andyboy179

find the gradient at the following points at the given (part2)

hi,
i don't understand how i would find the gradient at the following points at the given points:
y=3/x+2x+1 x=7

i know i would do:
y=3x^-1+2x+1
dy/dx=-3x^-2+2

im stuck after this because is i substitute it it looks like this:
dy/dx=-21^-2+2

what would i do from here??

thanks!
October 9th 2011, 04:56 AM
Siron

Re: find the gradient at the following points at the given (part2)

Is $y=\frac{3}{x+2x+1}$ or $y=\frac{3}{x}+2x+1$ ?
October 9th 2011, 04:57 AM
andyboy179

Re: find the gradient at the following points at the given (part2)

the second one, soory for the confusion!
October 9th 2011, 05:05 AM
e^(i*pi)

Re: find the gradient at the following points at the given (part2)

Quote:

Originally Posted by andyboy179

hi,
i don't understand how i would find the gradient at the following points at the given points:
y=3/x+2x+1 x=7

i know i would do:
y=3x^-1+2x+1
dy/dx=-3x^-2+2

Correct

Quote:

im stuck after this because is i substitute it it looks like this:
dy/dx=-21^-2+2

what would i do from here??

thanks!

That's an incorrect substitution: $-3x^{-2} +2 = -\dfrac{3}{x^2} + 2$ . You appear to have included -3 in the exponent which is not the case.
October 9th 2011, 05:07 AM
andyboy179

Re: find the gradient at the following points at the given (part2)

i tought i have to sub 7 into it so i did -3^-2x7= -21^-2. if the top part is correct how would i find the gradient?
October 9th 2011, 05:10 AM
e^(i*pi)

Re: find the gradient at the following points at the given (part2)

Quote:

Originally Posted by andyboy179

i tought i have to sub 7 into it so i did -3^-2x7= -21^-2. if the top part is correct how would i find the gradient?

-3 is not squared, only the 7 is squared. What you want to do is $-3 \times \left(7^{-2}\right)$
October 9th 2011, 05:14 AM
andyboy179

Re: find the gradient at the following points at the given (part2)

oh, so it would be 7^2= 49 then dy/dx=-3/49+2?
October 9th 2011, 05:30 AM
Siron

Re: find the gradient at the following points at the given (part2)

Correct!
October 9th 2011, 05:34 AM
andyboy179

Re: find the gradient at the following points at the given (part2)

so is dy/dx=-3/49+2 the gradient?
October 9th 2011, 05:37 AM
Siron

Re: find the gradient at the following points at the given (part2)

Quote:

Originally Posted by andyboy179

so is dy/dx=-3/49+2 the gradient?

Indeed! The gradient of the tangent line in the point x=7
October 9th 2011, 05:39 AM
e^(i*pi)

Re: find the gradient at the following points at the given (part2)

Quote:

Originally Posted by andyboy179

so is dy/dx=-3/49+2 the gradient?

Yes although since they are both numbers you should combine like terms to simplify your answer. I suggest writing $2 = \dfrac{98}{49}$ and get $\dfrac{-3}{49} + \dfrac{98}{49} = \dfrac{95}{49}$