Question

Find an equation of the tangent line to
y = ((sqrt2))^x at x = 4.

Answer 1

is it

Answer 2

So the equation of the tangent line is found by first finding the rate of change (slope) of the equation at that point so you will have to use Calculus. So you can express the deriviative as \[{dy \over dx} = {d \over dx } [\sqrt (2)^x] = \sqrt(2)^x*\ln(\sqrt(2))\] and then evaluate it at the point of interest whicwill yield the slope of the function at that point. Then you need to use a point to figure out your y intercept. and get the full equation of the line tangent to the function at that point.

Answer 3

so what is it?

Answer 4

\[(\sqrt{2})^x\]

Answer 5

Yeah...after that just use the slope-intercept formula to find the equation of the line. y-y1 = m(x-x1) where m is the slope of the tangent line to the function at that point.