Determining equation to the normal

Question

How would I determine the equation to the normal to the curve y=√5x when x=20?

Answer 1

y' = √5/2x^-1/2. At x = 20 y' = √5/2·1/√20 = 1/4. At x = 20 y = 10. Slope m of normal line: m = -1/y' = - 4.

Equation of normal line: y = 10 - 4(x - 20); y = - 4x + 90

Answer 2

Hi Annet B. You need:

1) Evaluate the original function at x=20.

Is the original function f(x) = (5x)^0.5 or is it 5^0.5 * x ? Makes a difference! Advice: if you use the sqrt symbol, ALWAYS enclose the entire argument in parentheses. That's unambiguous.

2) Take the first derivative of the function, and evaluate it at x=20. That's the tangent; if it has value m, the perpendicular has value - 1 / m .

3) You now have a point and a slope -- set into a standard formula and convert to a different formula type if desired.

Anne B., you should have encountered all these procedures before.?

-- Cheers, -- Mr. d.