1. Need help

Find the equation of the tangent to the curve y= 4^x +1 at the point (0,4).

The answer from the textbook is 4 ln 4 * x- y+ 4=0 .

I'm not sure how to get that answer. Any help will be greatly appreciated.

2. Re: Need help

Originally Posted by Bongo
Find the equation of the tangent to the curve y= 4^x +1 at the point (0,4).

The answer from the textbook is 4 ln 4 * x- y+ 4=0 .

I'm not sure how to get that answer. Any help will be greatly appreciated.
$\noindent The point (0, 4) does not lie on that curve, because 4^{0} + 1 \neq 4.$

3. Re: Need help

Originally Posted by Bongo
Find the equation of the tangent to the curve y= 4^x +1 at the point (0,4).

The answer from the textbook is 4 ln 4 * x- y+ 4=0 .

I'm not sure how to get that answer. Any help will be greatly appreciated.
$\noindent In general though, to find the equation of a tangent line at the point (a, f(a)) on the graph y = f(x), all you need to work out is the slope of the tangent line. Once you know this, since you know a point on the line as well (namely (a,f(a))), you can write down the equation of the line. (This is because if we know the slope and a point on a line, then we can write down its equation.)$

$\noindent As long as you know how to differentiate the function f(x) = 4^{x} + 1, you should have the tools required to find equations of tangents on the given curve.$

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