If an equation of the tangent line to the curve at the point where
E) None of these

Question

If an equation of the tangent line to the curve  at the point where  
E) None of these

Quizplus · Accepted Answer

To find the equation of the tangent line, we need to find the derivative of the function at the given point. 
f(x) = ln(x^4 + 16), so 
f'(x) = 4x^3 / (x^4 + 16)
At the point (1, ln(17)), we have x = 1, so 
f'(1) = 4 / 17. 
Using the point-slope form of the equation of a line, we can find the equation of the tangent line: 
y - ln(17) = (4/17) (x - 1)
y = (4/17) x - (4/17) + ln(17)
Simplify: 
y = (4/17) x + (13/17) - (4/17)
y = (4/17) x + 9/17
The corresponding answer choice is D.

If an Equation of the Tangent Line to the Curve