Find an equation of the tangent line to the curve at the given point. y = x , (16, 4) Step 1 To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (16, 4), we know that (16, 4) is a point on the line. So we just need to find its slope. The slope of a tangent line to f(x) at x = a can be found using the formula mtan = lim x→a f(x) − f(a) x − a . In this situation, the function is f(x) = and a =

The question is incomplete. The complete question is:

Find an equation of the tangent line to the curve y = at the given point (16,4). To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (16,4) we know that (16,4) is a point on the line. So we just need to find its slope. The slope of a tangent line to f(x) at x = a can be found using the formula m tan = lim x↔a f(x) - f(a)/ x - a.

y =

Step-by-step explanation: The tangent line is a line that intercepts a curve in only one point. The point-slope formula for a line is , where m is the slope of the line and can be calculated by the first derivative of the given curve. For this case:

y =

f'(x) =

f'(x) =

At point (16,4), the slope will be:

m = f'(16) =

m =

With slope and a point, the line function will be:

y - 4 = (x - 16)

y = - 2 + 4

y = + 2

The tangent line to the curve is y = x/8 + 2

the first option is the answer.