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!

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

Is $\displaystyle y=\frac{3}{x+2x+1}$ or $\displaystyle y=\frac{3}{x}+2x+1$ ?

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

the second one, soory for the confusion!

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: $\displaystyle -3x^{-2} +2 = -\dfrac{3}{x^2} + 2$. You appear to have included -3 in the exponent which is not the case.

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?

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 $\displaystyle -3 \times \left(7^{-2}\right)$

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?

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

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

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

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

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 $\displaystyle 2 = \dfrac{98}{49}$ and get $\displaystyle \dfrac{-3}{49} + \dfrac{98}{49} = \dfrac{95}{49}$