Question

Asked Oct 10, 2019

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Find the equation of the tangent line to the graph of f(x)=2xln(x+8) at x=6.

Step 1

Equation of the tangent line to the curve y = f(x) at the point (a, b) will be given by

(y - b) / (x - a) = f'(x = a)

Step 2

f(x) = 2xln(x+8)

a = 6

b = f(a) = 2 x 6 x ln(6 + 8) = 12 x ln(14) = 31.67

Step 3

f'(x) = 2ln(x + 8) + 2x / (x + 8)

- Recall the product rule of differentiation
- Recall that d[ln(x)] / dx ...

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