Good evening folks.
f(x) = 3^x - x^3
For what value of x, is the tangent to the curve parallel to the secant through (0,1) and (3,0)?
Do I find the slop between those 2 points and set it equal to the derivative of the original function?
This is as far as I got and i lost confidence that i was doing the right thing..
3^x(ln3)-3x^2=-1/3 ... multiplied both sides by 3 to get rid of the fraction
9^x(ln3) - 9x^2 = -1
log(9^x(ln3) + 1) = log(9x^2)
xlog9(ln3) + log(1) = 2log9x
did I royally screw up somewhere?
I don't think you can split a log up like that. Log(a+b) isn't Log(a) + Log(b)
By the way, here are the answers for your eqaution: solve 3^x ln(3) -3x^2 = (-1/3) for x - Wolfram|Alpha