For the curve with the equation 𝑦 = 𝜋√𝑥/ 2 , find the equation of the tangent at 𝑥 = 1.

Question

For the curve with the equation 𝑦 = 𝜋√𝑥/2 , find the equation of the tangent at 𝑥 = 1.

Answer 1

Anytime you see a request for tangent line means "take the derivative". (I'm sure you are aware that the value of the derivative at a point is the slope of the tangent line at that point.)

y = π(x/2)^1/2

Use the power rule and the chain rule to get the derivative:

y' = 0.25π/(x/2)^1/2 and plug in x = 1 to get the slope. m = 0.25π√2

So y = (0.25π√2)x + b.

To find b, first find f(1) which is 0.5π√2 then plug in the y value (0.5π√2) and the x value(1) into the equation y = (0.25π√2)x + b.to get:

0.5π√2 = 0.25π√2 + b to get b and plug that into the equation to get the complete equation of the line