`h(t) = sec(t)/t, (pi,-1/pi)` Evaluate the derivative of the function at the given point. Use a graphing utility to verify your result.
You need to evaluate the equation of the tangent line to the curve `f(t) =(sec t)/t` , at the point `(pi, -1/(pi)), ` using the following formula, such that:
`f(t) - f(pi) = f'(pi)(t - pi)`
Notice that `f(pi)=1/(pi).`
You need to evaluate f'(t), using the quotient rule, and then `f'(pi):`
`f'(t) = ((sec t)'*t- (sec t)*(t)')/(t^2)`
`f'(t) = (t*sec t*tan t - sec t)/(t^2)`
`f'(pi)= (pi*1/(cos pi)* tan pi - 1/(cos pi))/(pi^2)`
`cos pi = -1 and tan pi = 0`
You need to replace the values into the equation of tangent line:
`f(t) - 1/(pi) = (1)/(pi^2)*(t - pi)`
`f(t) = 1/(pi) + t/(pi^2) - 1/(pi)`
reducing like terms yields:
`f(t) = t/(pi^2) `
Hence, evaluating the equation of the tangent line to te given curve , at the given point, yields `f(t) = t/(pi^2) ` .