Thread: Determine the general equation of the secant from any point - Help!

1. Determine the general equation of the secant from any point - Help!

I have to find the general equation of a secant from any point (A,f(A)) to the point on f(x) = $\displaystyle 4^x$ where x = 2. That point is (2,16) Can someone help me develop this equation. I have an example. But they use the point (4,4) so its hard to tell what is the x and what is the y and how they are expanded and everything.

2. Equation of a line through a point (h,k) and with a given slope "m" is given by

(y-k) = m (x-h)

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Slope of a tangent at any point h on 4^x is given using differentiation of f(x)..

f(x) = 4^x

f'(x) = 4^x ln(4)

So

$\displaystyle f'(h) = 4^h \cdot ln(4)$

Hence the value of m in your question at any point (h,k) " lying on the curve": is

$\displaystyle m = 4^h \cdot ln(4)$

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So equation of tangent is

$\displaystyle (y-k) = 4^h \cdot ln(4) \cdot (x-h)$

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(h,k) is ( 2,16) in this particular problem.

Still in trouble feel free to ask.