Question

g(x)=sqrt(x)*(2x^2-4) when x=4

Derivatives.
I have to find the equation of the tangent line.

Answer 1

\[g(x)=\sqrt{x}(2x^2-4)\]

Answer 2

Distribute it then product rule afterwards?

Answer 3

I just feel like my slope is wrong. Especially for the equation

Answer 4

Or do i plug in the 4 once I find the derivative to find the slope?

Answer 5

Once you differentiate that that function and plugged x=4 in, you will get your slope \(\frac{dy}{dx}\)

Answer 6

\[g(x)=\sqrt{x} \left(2 x^2-4\right)\]
\[g'(x)=\frac{5 x^2-2}{\sqrt{x}}\]

Answer 7

Then how would I find the y intercept? Do I plug the x back into the original equation?

Answer 8

When x=4,
\[g'(x)=\frac{5 x^2-2}{\sqrt{x}}=39\]

Answer 9

Yeah I got 39 as well for the slope.

Answer 10

Use x=4 on g(x) to find the 'y' value, then once you've got a coordinate, and a slope, you can create an equation \((y-y_1)=m(x-x_1)\)

Answer 11

Thank you so much. This makes so much more sense now!

Answer 12

Cheers

Answer 13

Here is a graph of the tangent line