Question

find the equation of the tangent line to the curve f(x)=(2/(sqrtx))-2(sqrtx)^3 at the given point (4,-15)

Answer 1

Step 1 :

The curve is and the point is .

Consider .

Apply derivative on each side with respect to .

At the point , .

This is the slope of the tangent line to the curve at the point .

.

Step 2 :

Find the tangent line using the point-slope form : , where is the slope.

Substitute the values and in point-slope form.

Thus, the tangent line is .

Solution :

The tangent line is .