I need to find the equation of the tangent line at the point:
s(t)=Int, at t=5

Question

I need to find the equation of the tangent line at the point:
s(t)=Int, at t=5

turingtest · Answer

the equation from a straight line from algebra is$$y-y_1=m(x-x_1)$$where m is the slope, and y is the value of the function at that point
since we know the slop at a point is given by the derivative at that point, we can make a calculus version of this formula for the equation of the tangent at some point:$$y-f(x_1)=f'(x_1)(x-x_1)$$so what is $$f'(x)$$ in your case?

anonymous · Answer

1/t^In

turingtest · Answer

?
no that's not$$\frac d{dt}\ln t$$try again please

anonymous · Answer

Int/sqtr t

mikey · Answer

The derivative of ln(t) is 1/t....which gives you the slope of a tangent line at a point on the curve ln(t). It's then just a matter of algebra to find the equation for the tangent line given a point.