Thread: 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!

Is or ?

the second one, soory for the confusion!

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

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: . You appear to have included -3 in the exponent which is not the case.

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?

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

oh, so it would be 7^2= 49 then dy/dx=-3/49+2?

Correct!

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

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

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 and get