Thread: slope of line tanget to graph

The slope of the line tangent to the graph of 3x^2 + 5ln(y) = 12 at (2,1) is...

a) -12/5
b) 12/5
c) 5/12
d) 12
e) -7


**Im not particularly differentiating y in respect to x and could use some help.

Originally Posted by DINOCALC09

The slope of the line tangent to the graph of 3x^2 + 5ln(y) = 12 at (2,1) is...

a) -12/5
b) 12/5
c) 5/12
d) 12
e) -7


**Im not particularly differentiating y in respect to x and could use some help.

how else would you do it?

i'd differentiate implicitly here and then plug in x = 2, y = 1 into the formula i get.




differentiating implicitly we get:



now solve for dy/dx and plug in the required x- and y-values

Originally Posted by Jhevon

how else would you do it?

i'd differentiate implicitly here and then plug in x = 2, y = 1 into the formula i get.




differentiating implicitly we get:



now solve for dy/dx and plug in the required x- and y-values

dy/dx = -6x/(5/y)?

Originally Posted by DINOCALC09

dy/dx = -6x/(5/y)?

no.

........move the 6x to the other side by subtracting it from both sides

........multiply both sides by

so as im understanding, the answer is (A) or -12/5

Originally Posted by DINOCALC09

so as im understanding, the answer is (A) or -12/5

yes