Question

find the equation the tangent f(x)=4x-8√x at x=16​

Answer 1

Answer:

To find the tangent line we need a point and slope. As tangent passes through the point whose x coordinate is 4, the y coordinate is given by

When x = 4

y = (16*4)-(4√4) = 64 -8 =56

y = 6

Te point is (4, 56)

To find slope we have to find the derivative of g(x) at (4,56)

g’(x) = 16 -(4/(2√x))

g’(x) = 16 - (2/√x)

Slope of the line, m = 16 -(2/√4)

m = 15

Eqution of tangent is

y - y0 = m(x- x0)

where x0 =4, y0 =56 and m =15

y - 56 = 15(x - 4)

y - 56 = 15x - 60

y - 15x + 4 = 0 is the required tangent line