[Risolto] eq retta

Il grafico della funzione
* f(x) = y = tg(4*x) + 9^x
ha pendenza
* m(x) = dy/dx = ln(9)*9^x + 4/cos^2(4*x)
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All'ascissa x = 0.7 = 7/10 si ha
* f(7/10) = y = tg(14/5) + 9^(7/10) ~= 43/10 ~= 4.3
* m(7/10) = ln(9)*9^(7/10) + 4/cos^2(14/5) ~= 5113/347 ~= 14.7349
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La retta t di pendenza m = m(7/10) per il punto T(7/10, h = f(7/10)) è
* t ≡ y = h + m*(x - 7/10) ≡
≡ y = (tg(14/5) + 9^(7/10)) + (ln(9)*9^(7/10) + 4/cos^2(14/5))*(x - 7/10)
ed ha intercetta
* q = h - (7/10)*m =
= tg(14/5) + 9^(7/10) - (7/10)*(ln(9)*9^(7/10) + 4/cos^2(14/5)) ~=
~= - 3759/625 ~= - 6.0144
http://www.wolframalpha.com/input?i=%5By%3Dtg%284*x%29--9%5Ex%2Cy%3D%28tg%2814%2F5%29--9%5E%287%2F10%29%29--%28ln%289%29*9%5E%287%2F10%29--4%2Fcos%5E2%2814%2F5%29%29*%28x-7%2F10%29%5D

y = TAN(4·x) + 9^x

y = TAN(4·0.7) + 9^0.7

y = 4.300006890------> [0.7, 4.3]

y' = dy/dx= 2·3^(2·x)·LN(3) + 4/COS(4·x)^2

m=2·3^(2·0.7)·LN(3) + 4/COS(4·0.7)^2 = 14.735 (circa)

Retta tangente:

y - 4.3 = 14.735·(x - 0.7)----> y = 14.735·x - 6.0145